What about the Vehicle Assembly Building at NASA’s Kennedy Space Center (KSC).
https://science.ksc.nasa.gov/facilities/vab.html
The VAB covers 3.25 hectares (8 acres). It is 160 meters (525 ft 10 in) tall, 218 meters (716 ft 6 in) long and 158 meters (518 ft) wide. It encloses 3,664,883 cubic meters (129,428,000 cubic feet) of space.
The building has at least 40 MW of air conditioning equipment, including 125 ventilatorson the roof supported by four large air handlers (four cylindrical structures west of the building) to keep moisture under control. Air in the building can be completely replaced every hour. The interior volume of the building is so vast that it has its own weather, including “rain clouds form[ing] below the ceiling on very humid days”
https://en.wikipedia.org/wiki/Vehicle_Assembly_Building
But I dont know if you really can visit it (https://space.nss.org/you-too-can-visit-the-vehicle-assembly-building/)
I wanted to mention indoor ski slope, like the biggest Alpincenter Bottrop, but apparently a ski slope is way smaller than a mall… If the roof is at 4m we stand at a volume of about 77k cubic meters.
Maybe stretching the spirit of the question (not man-made, entrance fee ~$3000 USD), but perhaps the Hang Sơn Đoòng Cave – it has a continuously connected volume of 38.4 million m³.
Boeing’s Everett Production Facility is the largest building in the world by volume at ~13.4m cubic meters. It is climate controlled.
At approximately 98 acres, it is larger than Disneyland but smaller than Magic Kingdom.
Public tours are available for a fee.
The O2 arena in London is an air condiditoned space of 2.79 million cubic meters. Looking at Wikipedia’s list of largest buildings, this may well be the largest-volume building that is both publicly accessible and air conditioned. There are only 8 buildings larger in volume than the O2, but their main spaces are either not publicly accessible, not air conditioned, or both (unclear about the Tropical Islands Resort mentioned in another answer, but it would seem reasonable to forego air conditioning for an indoor water park located in a cold climate).
I have not yet been able to find the volume of the Iran Mall, in Tehran, but its area is 1.4 million square meters, and it appears to be multi-floor.
Based on a comment by Neusser, 1.4 million square meters is the total floor area, so I can only count one floor height. At 3 meter height, that would give it a total volume of about 4.2 million cubic meters, 5.6 million cubic meters at 4 meters.
I would think it is the Tropical Island Resort in Germany. Apparently it has 5.5 million m³ of volume space. It is kept around 26°C all year around.
I’ll kick off with one:
The Flower Dome at Singapore’s Gardens by the Bay is the largest greenhouse in the world as listed in the 2015 Guinness Book of World Records, clocking in at 195,000㎥ of space kept to 23-25°C all year around. For comparison, ambient temperatures in Singapore hover around 30°C.
Credit:stackoverflow.com‘