I have somewhat of a reptile room going on, more so an Aquarium room that was not 100% full that shares space with my Cham's.
If you have an unfinished room you're set. If you can, replace the drywall with closed foam insulation and cut it to size to fit between the beams. This will provide you two things, much more resilient insulation that won't mold as well as a higher R value so that you don't have to worry about heat from that room escaping easily to other parts of the house, and/or cool pushing its way in from either the AC or just cooler rooms on the same floor.
Here is what I'm talking about:
When I first moved into my home over a year ago now and I wanted to get back into breeding some rare/oddball freshwater aquarium fish as well as propagating aquarium plants I converted a storage/utility room for exactly that purpose. I first went through and cut some insulation to the right sizes and fit them between the beams. Some of you might ask why I didn't just lay sheets across the boards, well to optimize the available space. 2" thick insulation would mean I would lose 2" of space all around once all surfaces were covered. Once the 2" insulation went up I taped the seams with insulating metal tape. This would allow me to create a full seal between the joists and the insulation as well as creating a vapor barrier where the humidity could not escape the room as the joists were now also sealed. I did this between every joist, but sadly I don't have complete pictures as I was juggling moving old aquariums from the old place into the new place.
When it came to the ceiling what I did was get attic grade fiber insulation rolls and cut pieces to stuff right above the wall joists to prevent heat from escaping from the gaps that lead to the floor joists above, i.e. the joists that hold up my first floor above the basement. Once all those gaps were insulated I moved to stapling up 8 mil plastic sheeting to the ceiling as I wanted to create a vapor barrier, but have easy access to piping and electrical that was above if I ever needed to get to it. I taped up all seams with the same metallic insulating tape.
As this room is on a concrete slab and there are no HVAC vents going here, the room is on its own climate control. One thing I'm going to make very clear, do the math on your electrical needs so you have the right breakers so you don't start an electrical fire or keep popping breakers. When I started this it was in the summer and the basement would stay in the low 60's since the one wall you don't see is concrete and is surrounded by dirt on the other side which keeps the wall insulated from the exterior elements. When it came to winter, the room would drop to the 50's and I ended up wanting to add some ambient heat to keep my internal heating needs per tank down. From there I added a room heater (forced air over coils initially) and ended up having to play the breaker dance which is annoying. Ended up moving that heater to an oil radiator type heater to keep the room at an ambient 65 degrees in the winter. Another thing you can see in the picture above is something that all closed rooms will need when water is involved, a dehumidifier. Once you have a ton of sources of water, you're not going to be needing a humidifier, but more so a dehumidifier to keep things in check and to make sure that the room isn't perfect for mold to grow in.
Things that are additionally helpful are water filtration/storage units if you plan on using a misting system. I myself use RO/DI water for other things besides the Cham's so you won't need the 120 gallon storage I'm using, but a unit plus 35 gallons of storage (one of the smallest water storage tanks on the market that isn't a 5 gallon bucket) would suffice and last most people a long time. I myself have my RO/DI unit tapped to my cold water supply and then fed to a drilled feed into my 120 gallon storage to a float switch so I always have water stored and never have to go and rig things up to get the water filter ready to go and then produce my clear water and drainage effluent. Why am I recommending RO/DI? Well it keeps the pumps from calcifying as well as the nozzles from building up mineral deposits so I don't have to soak them in any acidic solution to keep them running efficiently consistently.
I know what I've done isn't what most are after, but I had the space and it fit with another hobby so I made it work. Now I have a room that without any hardware running (mainly lights) will stay in the mid 60's and get up to 75 with lights running. I don't have to worry about cold blasts from AC throwing anything off or my HVAC in the winter drying the room's air below 40%.
Besides my baby rack which I don't have pictures of, here are the adults/sub adults in their nook of the room.
Lots of things are changing and the enclosures are always having plants added/removed depending on what I'm doing that day (i.e. hacking up plants to propagate or if something is needing to be trimmed to fit such as Hibiscus)