When I am making a tool bit out of tungsten carbide, do I have to keep it
cool? Does heat change it's hardness, or does this just apply to tempered
steel?

Carbide grinding should be done very wet or dry. If you have intermittent
cooling thermal shock will crack it.

I have had poor luck grinding brazed carbide toolbits with silicon
carbide grinding(green) wheels. They cut slow and edge is pretty rough.
Diamond wheels work very well.

chuck