Cool idea!!
It runs cold forI don't know what's wrong with your hot water at all your houses
My tap water will scald you. I use a thin cotton barber towel with a green stripe. A light squeeze to get out the excess water and apply to my face. The best part is at the end of the shave and I have toweled off the excess cream remnants...I will wave the towel back and forth to cool it and apply it to my face to close the pores. It's just not a shave without it.