I have a few concerns (actually, many) regarding the use of space heaters. In this situation, using a space heater is a recipe for disaster (even if it has a supposed "turn off" feature if tipped; it isn't fail-proof). Space heaters can very quickly overheat a small area like a closet even with a thermostat.
Instead, if you are going to do this right, here is what I would recommend:
1) Use a pro product radiant heat panel mounted to the inside ceiling of the wall making sure that no cords are exposed. This will provide an excellent heat source. Depending on the temps of the floor, a thermostatically controlled pig blanket like a Kane heat mat will work great (once again, make sure that no cords are exposed).
2) I would make sure that some sort of full spectrum fluorescent light is installed as this will provide a great light source w/out adding extra heat.
3) Get rid of that old carpet! This closet is going to need to maintain a high amount of humidity and carpet will only harbor lots of bacteria and mold. I would cover the floor w/ceramic tile; something that can be easily cleaned and disinfected as needed. If the tile gets too cool, you can put layers of newspaper over it for insulation.
4) Ventilation: how are you going to provide adequate air flow? Hopefully, you have excellent air flow; otherwise, the closet could be a nice festering ground for all kinds of air borne pathogens. A JWR Air Cleaner would be an excellent investment.
5) HUMIDITY: I would recommend a JWR ultrasonic vaporizer; one of the only products that provides humidity while at the same time pumping out ZERO harmful bacteria like most other humidifiers and vaporizers.
6) SECURITY: How will this closet be secure? Make sure that the door is 100% escapeproof.
There are other considerations but these are the highest priority to consider. Good luck, Rob
Rob Carmichael, Curator
The Wildlife Discovery Center at Elawa Farm
City of Lake Forest Parks & Recreation (IL)