What were the dimensions of the Jewish Temple in Jerusalem?

Here is some evidence for the total vertical extension of the temple and for the temple mount:

• This site discusses 5 theories about the location of the Jewish temple; and discussing the theory of Dr. Martin, it says:

I read where Dr. Martin said that the southeast corner was 300 cubits high according to Josephus and was built into the bedrock of the Kidron valley. The text does not say that at all. Josephus tells us:

“The lowest part of this (lower court of the temple) was erected to the height of 300 cubits, and in some places more; yet did not the entire depth of the foundations appear, for they as being desirous to make them on a level with the narrow streets of the city; wherein they made use of stones of forty cubits in magnitude;”

This of course was speaking of the southwest corner where there were narrow streets of the city to bring the level up to. Not the Southeast comer where there were no streets.

_{— Temple Mount Location, Five Temple Location Theories.}

So Josephus claimed that the retaining wall of the Temple Mount was 300 cubits tall in the southwest corner!

• This site discusses various descriptions of the temple(s) in Josephus and other sources.

• A cubit was a length of about a man's forearm:

The cubit was an ancient unit of length based on the distance from the elbow to the middle finger. It was primarily associated with the Sumerians, Egyptians and Israelites. "Cubits" is found in the Bible re: Noah's Ark, Ark of the Covenant, Tabernacle, Solomon's Temple. The common cubit was divided into 6 palms × 4 fingers = 24 digits. Royal cubits added a palm for 7 palms × 4 fingers = 28 digits. These lengths typically ranged from 444 to 529.2 mm, with an ancient Roman cubit being as long as 120 cm.

Cubits of various lengths were employed in many parts of the world in antiquity, during the Middle Ages and as recently as early modern times. The term is still used in hedge-laying, the length of the forearm being frequently used to determine the interval between stakes placed within the hedge.

_{— Wikipedia, Cubit.}

The standard of the cubit (Hebrew: אמה‎) in different countries and in different ages has varied. This realization led the rabbis of the 2nd century CE to clarify the length of their cubit, saying that the measure of the cubit of which they have spoken "applies to the cubit of middle-size". In this case, the requirement is to make use of a standard 6 handbreadths to each cubit, and which handbreadth was not to be confused with an outstretched palm, but rather one that was clinched and which handbreadth has the standard width of 4 fingerbreadths (each fingerbreadth being equivalent to the width of a thumb, about 2.25 cm). This puts the handbreadth at roughly 9 centimetres (3.5 in), and 6 handbreadths (1 cubit) at 54 centimetres (21 in)

_{— Wikipedia, Rabbinical cubit.}

The portico at the entrance of the temple was usually described at twice the height of the sanctuary itself. The temple was 30 or 60 cubits high, and the portico was 60 or 120 cubits high. At 18 to 21 inches per cubit, 30 cubits would be 540 to 630 inches, or 45 to 52.5 feet, or 13.7 to 16 meters, tall. 60 cubits would be 1,080 to 1,260 inches, or 90 to 105 feet, or 27.5 to 32 meters, tall. 120 cubits would be 2,160 to 2,520 inches, or 180 to 210 feet, or 55 to 64 meters, tall.

So the portico at the front of the temple would have been a decent sized tower, whether it was 90 to 105, or 180 to 210, feet tall.

• In the Wars of the Jews, Book V, Chapter 5, Josephus describes the Temple of Herod beginning with the temple platform:

Now this temple, as I have already said, was built upon a strong hill. At first the plain at the top was hardly sufficient for the holy house and the altar, for the ground about it was very uneven, and like a precipice; but when king Solomon, who was the person that built the temple, had built a wall to it on its east side, there was then added one cloister founded on a bank cast up for it, and on the other parts the holy house stood naked. But in future ages the people added new banks, 12 and the hill became a larger plain. They then broke down the wall on the north side, and took in as much as sufficed afterward for the compass of the entire temple. And when they had built walls on three sides of the temple round about, from the bottom of the hill, and had performed a work that was greater than could be hoped for, [in which work long ages were spent by them, as well as all their sacred treasures were exhausted, which were still replenished by those tributes which were sent to God from the whole habitable earth,] they then encompassed their upper courts with cloisters, as well as they [afterward] did the lowest [court of the] temple. The lowest part of this was erected to the height of three hundred cubits, and in some places more; yet did not the entire depth of the foundations appear, for they brought earth, and filled up the valleys, as being desirous to make them on a level with the narrow streets of the city; wherein they made use of stones of forty cubits in magnitude; for the great plenty of money they then had, and the liberality of the people, made this attempt of theirs to succeed to an incredible degree; and what could not be so much as hoped for as ever to be accomplished, was, by perseverance and length of time, brought to perfection.

_{— Josephus, Wars of the Jews, Book V, Chapter 5, Paragraph 1.}

So Josephus wrote that the retaining wall of the temple mount was up to 300 cubits high where the valley was lowest. At at 18 to 21 inches per cubit, the 300 cubit high wall would have been about 5,400 to 6,300 inches, or 450 to 525 feet, or 137 to 160 meters, tall.

And according to Josephus, the summit of Herod's temple would have been about 630 to 735 feet, or 192 to 224 meters, above the very bottom of the foundations of the retaining wall. That is a considerable vertical distance - if Josephus is accurate.

• Josephus may have exaggerated the height of the highest portions of the retaining wall:

At the Western Wall Plaza, the total height of the Wall from its foundation is estimated at 105 feet (32 m), with the above-ground section standing approximately 62 feet (19 m) high. The Wall consists of 45 stone courses, 28 of them above ground and 17 underground. The first seven above-ground layers are from the Herodian period.

_{— Wikipedia, ​Western Wall: Height, courses, building stones​​​.}

But maybe the bedrock was much lower in other parts of the wall.

Of course the majority of that height was the retaining wall of the enclosure, and the foundations of the temple were not on that wall, but a considerable distance within it. There is considerable controversy about where the temple stood in the temple enclosure, but it is certain it wasn't built on the retaining wall of the temple enclosure.

The temple itself was built atop a high platform that exists to this day. The Western Wall of this platform is 62 feet, or 19 metres high, but the foundation extends another 43 feet, or 13 metres, below ground, for a total height of 105 feet, or 32 metres.

According to the Jewish Encyclopedia:

The structure was 60 cubits long, 20 cubits wide, and 30 cubits high (I Kings vi. 2).
— TEMPLE OF SOLOMON - JewishEncyclopedia.com

Of the dimensions of this Temple there are given but few data. Hecatæus, a Greek writer contemporary with Alexander the Great, is quoted by Josephus ("Contra Ap." i. 22) as saying that the Temple area was enclosed by a wall a plethra, or 500 Greek feet, in length and 100 Greek cubits in breadth, i.e., 485½ × 145½ English feet.
— TEMPLE, THE SECOND - JewishEncyclopedia.com

The Temple proper as reconstructed by Herod was of the same dimensions as that of Solomon, viz.: 60 cubits long, 20 cubits wide, and 40 cubits high.
— TEMPLE OF HEROD - JewishEncyclopedia.com

A cubit is about 18 inches or 46 centimetres.

Here are the original plans:

And it came to pass in the four hundred and eightieth year after the children of Israel had come out of the land of Egypt, in the fourth year of Solomon’s reign over Israel, in the month of Ziv, which is the second month, that he began to build the house of the LORD. Now the house which King Solomon built for the LORD, its length was sixty cubits, its width twenty, and its height thirty cubits. The vestibule in front of the sanctuary of the house was twenty cubits long across the width of the house, and the width of the vestibule extended ten cubits from the front of the house. And he made for the house windows with beveled frames.

Against the wall of the temple he built chambers all around, against the walls of the temple, all around the sanctuary and the inner sanctuary. Thus he made side chambers all around it. The lowest chamber was five cubits wide, the middle was six cubits wide, and the third was seven cubits wide; for he made narrow ledges around the outside of the temple, so that the support beams would not be fastened into the walls of the temple. And the temple, when it was being built, was built with stone finished at the quarry, so that no hammer or chisel or any iron tool was heard in the temple while it was being built. The doorway for the middle story was on the right side of the temple. They went up by stairs to the middle story, and from the middle to the third.

So he built the temple and finished it, and he paneled the temple with beams and boards of cedar. And he built side chambers against the entire temple, each five cubits high; they were attached to the temple with cedar beams.
…
So Solomon built the temple and finished it. And he built the inside walls of the temple with cedar boards; from the floor of the temple to the ceiling he paneled the inside with wood; and he covered the floor of the temple with planks of cypress. Then he built the twenty-cubit room at the rear of the temple, from floor to ceiling, with cedar boards; he built it inside as the inner sanctuary, as the Most Holy Place. And in front of it the temple sanctuary was forty cubits long. The inside of the temple was cedar, carved with ornamental buds and open flowers. All was cedar; there was no stone to be seen. … [further details of the interior] …
— 1 Kings 6:1–18 (NKJV)