Is there scriptural basis for feelings such as "electricity", "fire", "heat" or "burning all over" reported in Pentecostal and Charismatic circles?

I regret that I can't speak specifically to Pentacostalism, which uses as one of its fundamental verses the experiences of the Day of Pentecost in the book of Acts (Acts 2:1-4), which appears to be more of an external experience than an internal (feelings) experience. But let's examine a couple of Biblical verses.

When the Lord shall have washed away the filth of the daughters of Zion, and shall have purged the blood of Jerusalem from the midst thereof by the spirit of judgment, and by the spirit of burning. (KJV Isa 4:4)

This appears to be speaking of the end-days when God shall restore Israel. He speaks of doing so by the "spirit of judgement" and the "spirit of burning." Part of any restoration must be (a) the individual's realization that past behavior was wrong and (b) some means of knowing that the new behavior is acceptable to God. I believe the spirit of judgement and the spirit of burning refer to (b). A person who successfully changes their lives to conform to the Gospel will know that their life is acceptable through a feeling (the "spirit of burning").

And they were astonished at his doctrine: for his word was with power. (KJV Luke 4:32)

My belief in this verse may be a bit more esoteric, but I believe it's valuable. The modern interpretations of the ancient Greek tend to favor the word "authority" over "power." But I've "spoken with authority" in my own profession (Engineering), speaking with both conviction and certainty — and I've never once had the reaction like that recorded in Scripture. Yes, Jesus did not come out of the Schools of Law, so it may be that they were simply surprised that He was as good a preacher as He was without that formal training — but I believe the Surprise had more to do with what they were feeling than what they were experiencing. And to support this idea, we have the following:

And they said one to another, Did not our heart burn within us, while he talked with us by the way, and while he opened to us the scriptures? (KJV Luke 24:32)

That's perhaps the most obvious of the scriptural references to a feeling (specifically a "burning," perhaps the "spirit of burning" spoken of by Isaiah).

And finally, the words of Paul.

And my speech and my preaching was not with enticing words of man’s wisdom, but in demonstration of the Spirit and of power: (KJV 1 Cor 2:4)

Paul talks about not simply speaking words, but those words being verified (a "demonstration") by the Spirit via some sort of power.

So, there is scriptural support for strong feelings, notably a feeling of "burning," that accompany the witness of the Holy Ghost to the preaching of the Word.

However…

In my experience, it can often be difficult to discern the difference between the Spirit and Showmanship. Humanity (and most certainly the devil) learned long ago that emotions can be manipulated. Those manipulations are the root of music, dance, drama, and other forms of entertainment. They're used for education, indoctrination (good and bad) — and frankly are tapped into for commercial marketing.

I believe it is for this purpose that God ensured the following verse was available to us today:

And he said, Go forth, and stand upon the mount before the Lord. And, behold, the Lord passed by, and a great and strong wind rent the mountains, and brake in pieces the rocks before the Lord; but the Lord was not in the wind: and after the wind an earthquake; but the Lord was not in the earthquake: and after the earthquake a fire; but the Lord was not in the fire: and after the fire a still small voice. (KJV 1 Kings 19:11-12)

As dramatic as that feeling of burning is (I know I have felt it), it must be discerned (analyzed, considered, tested) with patience, peace, and stillness. This secondary confirmation is so very important.

If any of you lack wisdom, let him ask of God, that giveth to all men liberally, and upbraideth not; and it shall be given him. But let him ask in faith, nothing wavering. For he that wavereth is like a wave of the sea driven with the wind and tossed. (KJV James 1:5-6)

Because that wavering is what allows us to think that we felt a spiritual burning when what we really experienced was showmanship. I suspect that if we could interview people who heard Adolph Hitler speak in 1937, they would have said they felt a burning, too.