I voted 'Hot'. I always preheat my cups with brew
water while I grind and build my shot. If I am going to make a pair of cappuccinos, they get filled with water and I hit the "beverage" button on the microwave for two drinks. For Americanos, a full cup, "beverage" button, dump about half the water and pull the shot on top. For Bodum double walls, I never heat them and they sit 'cold' in the cupboard.
If I make a press pot, I try to use any left over kettle water to warm my cup while the coffee steeps. At work, I use the hot water tap on the drip brewer to preheat my coffee mug (though I never drink the office coffee
I can't speak to "shocking" in a room temperature cup (although I think I've tasted it by adding espresso to milkshakes), and I don't care for a 'very hot' cup. I do tend to take my time drinking most beverages, so I like to extend that time a bit by not having the cup sink the heat from the beverage.
I've seen 5 minutes banted about as the recommended time for consuming a cup of coffee. No problem on the 'spro, but for a press pot or even an Americano, that's a little short for me.