They can handle water temps up close to 90 because we have them in several playa lakes down here in Texas where the water temps get that warm and also down to mid 40 degree water temps easily.
Bullheads can live any were. We have them in ponds here and lakes freeze over here. I currently have 1 in a tank with a bunch of blue channel cats there awesome fish to keep.
Bullheads are a family, not one species. The temp tolerance has mostly to do with the oxygen concentration in the water. Browns and yellows tolerate better than blacks - all three are northern. White bullhead and FL bullhead are southern species, more accustomed to warm water.