I've changed oil when the engine was hot and when it was cold. I usually do it on a cold engine that has been sitting overnight. At least 90% of the time all I've done is started the engine long enough to to pull the car up on ramps then cut it off. Probably a maximum of 1 minute. I usually let it drain until it's a slow drip, somewhere around 5 minutes I guess. While the oil pan is draining I remove the filter, wipe off the filter mounting surface and put the new filter on, By the time I've changed the filter and cleaned up any oil that spills on car parts from it I'm ready to put the plug back in the oil pan and refill the sump.