how big/many lights are you running? have you had the opportunity to get temps in the room? do a dry (no plants in yet) running of your lights and check the max temp of the room. if you can keep that an ambient 70-80 degrees (or roughly the same temp as the rest of the house) my thoughts are that the only thing which would show up on FLIR is the actual lights. you can buy stuff which supposidly blocks the thermal signature, its like mylar but more expensive...
I have a closet of similar dimensions which has one outside wall, so i'm curious to learn also.