With a propane space heater the "exhaust" is vented right into the surrounding area. One of the major byproducts of propane is water - lots of it! And it won't take long before you get a good headache from the fumes (which even a paint mask won't help).

Virtually any heater - with the exception of hogh-efficiency furnaces - will use room air as combustion air. This means that anything in the room is exposed to the flame. Personally I wouldn't paint that large of a project anywhere near an open flame of any sort. On the other hand, if your paint's water based ...