No. Not hot. Warm. Warm lather is devine. You don't need it in Florida. But up North it's so nice to have warm lather on a cold morning. But that is the extent of "warm" that I use in my shave. All of my rinses are cold. Ice cold if possible. I don't need to heat up towels in the microwave because I always shave after a hot shower.
We can't get really cold water down here most of the year . Sometimes even our cold water is lukewarm.
Genuinely cold water to rinse with would probably be a good thing. The water we have most of the year isn't going to stop bleeding, for instance.
I'm so used to the heat and cold blooded I just can't deal with shaving in the cold anymore, and I'm too cheap to run the heater much.