I usually do it warm, a few minutes after a drive. I usually let it drain until the dripping pretty much stops (about 20 mins or so). Then, I put the plug back in, and change the filter. By this point, the exhaust has cooled so I don't burn myself too badly changing the filter. The stupid thing sits above the starter (gets oil on it every time, but hey, it won't rust). You have to reach up above one of the upper control arms next to 1 side of the Y-pipe.
The burn issue comes in when you actually loosen the filter, because it sits at a 45* angle (baseplate upwards), and you're reaching straight up under it, so you almost always get hot oil dumping down your arm when you pull the thing off. The one on Mom's Jeep with a 4.0 is so much easier. It's sideways to the block, so it's messy, but you can reach it from the top, so you don't get dripped on.
I was always taught to change it hot, as stuff will be held in suspension better, and you're less likely to end up with crud settling in the pan.