Only 30 minutes? I recently let my tegu (over 3 feet) roam my BOQ and decided to let him out for the night, there were no hiding spots available really and as big as he is, I figured everything would be ok. I set up the night heat lamp on my dresser along with some newspaper and his water bowl figuring he'd spend the night there, but of course he wanted to roam the room so I figured ok.. fell asleep and woke up the next day and he was nowhere in site. Looked under the dresser, behind the small refrigrator, under the bed, in my dvds box, not much else in the BOQ, frustrated I left for work, came home, looked a little more, nothing, then headed back to my parents house and came back the next day (I also setup the day heat lamps - UVA/UVB to replace the night light, hoping he'd come out to bask) and spent about 45 minutes tearing my BOQ apart, laundry, anything I could see. Finally I thought to look at my bed mattress and did the typical "pat search" (I'm used to this with inmates) and felt something bulky in there. Turning the mattress over, sure enough there was a hole in it and when I looked inside I saw my tegu in there. I had to cut open the mattress even more (ruining it) just to get him out.
After that, the only time he comes out now is when I'm with him, and when I'm not, back to the cage.
Back to the question at hand though, I agree with the suggestions offered, you could even just spend the day with him (if you're not the one painting) take him to a free room, the bathroom (as suggested) would be a great spot. He can't really hide anywhere in there and he'll have plenty of room to explore. You could fill up the tub with warm water and have him soak for a half hour or so as well. I soak with my tegu several times per week and he stays in (falling asleep most of the time) until I come to get him.