/opens_can-of-worms.... Warm as you like for most of us. Unless you're one of those weird cold water shavers. Welcome to TSD.
I use hot water for everything, regardless of the time of year. My only exception is if I Nick myself, which is the only time I use cold water for a rinse. I simply like warmer lather better than cold, so there isn't any result driven basis for my choice. Sent via mobile - Chris
I love cold lather shaving regardless of the time of year or seasons, trouble is you're just not as tough as you think you were any more for warm lather shavers.
When it's cold outside, I prefer warm lather & rinse. When it's hot, cool for both. Like preshave oil I tried either way and found it doesn't seem to change my results.
Here's a quote from the Art of Manliness article Garrette mentions above, and the reason I use hot water... "I did notice that my razor tugged on my whiskers a bit more than when I shave with hot water."
Cold water for everything. Coldest that the tap will produce. It's much colder in the Winter, obviously. Sometimes in the summer I'll use ice water because the tap water is just too warm. I feel it helps with irritation as well as being invigorating. To each his own! There's no right or wrong - use what you like!