Yeah, you could do it. Basically, you'd have to have the camera set to detect light outside the visible spectrum. IR would work, but you might not get the best resolution (they'd have to have some pretty advanced sensors), and you wouldn't be able to see anything that was room temperature.
A better option would probably be something like UV. Not actual UV, since that would be rather harmful to the occupant of the room, but something like that. Flood the room with a type of light that the camera can see but that a human can't. You wouldn't be able to see colors, but you could get a fairly good monochrome image of the whole room.
In fact, there are some video cameras that do something like that. They have a "nightshot" capability which basically works like night vision goggles, essentially increasing the camera's sensitivity to what little light there is, but they also have "super night shot," which dramatically increases the picture you get by emitting a beam of light invisible to the human eye. Looking it up, I see that they actually do use low-intensity IR light. You can even buy a seperate, more powerful IR emitter to allow you to do exactly what you're asking about. If you're curious, there's one
here .
Paul