I think I may have answered too quickly before. At first I was just going to tell k2dave: Yes, but at such low temperatures you wouldn’t be able to see the Flame. But now I’m thinking that if you can’t see it, then it isn’t really a flame, is it?
Everything that I said in my previous answer would still be correct if we could all walk around with those military infrared goggles all the time because then we could see the flames from all those low temperature reactions. But as we can’t then I don’t think it is proper to refer to those as fires.
So - BETTER ANSWER (I hope): bodies will first radiate in the visible range at 400C (barely visible). For reference, candles generally burn at 1700C.
I guess it all depends on exactly how you define fire and flame.