Distal radius wrist fracture, I now in cast 3 weeks. Why my fingers feel less painful when I run them under hot water. Is it ok to run under hot water?

Loosens fingers. OK to run fingers under hot water as long as you don't get your cast wet. Exercising your fingers gently is a good idea.
Gentle finger range. of motion often feels better for stiff fingers with warm water, moist heat. So as long as one is careful not to burn the skin and one is careful to keep the cast fairly dry then warm water will feel good on arthritc joints in the cold, especially in the early AM. too much heat though can swell and make the cast tight. At the end of the day if fingers get too swollen then ice can be used too.