I have always changed the oil in my vehicles with the engine hot, because the manuals always say to let the engine reach normal operating temperature first. Oil change instructions all over the internet say this, too. I've never done it cold because everything says not to, and I never questioned this.
I've burned myself on more than one occasion, last night being the most recent, and it makes it trickier to get the filter out when you have to play Operation on a hot car.
Why do I have to change the oil when the engine is hot and what happens if I do it cold?