I have always done it with a warm engine. I have never thought to run a little oil threw it before putting the plug back in. I will do that when I do my LIM gasket, to make sure that there is no coolant in there.
I forgot to mention this earlier. When doing a LIM gasket job, the absolute best way to flush out any coolant out of the motor. Is with the plug pulled on the pan (obviously) and before reinstalling the LIM, dump 1 or 2 quarts of fresh motor oil into the lifter valley and let it drain out. This has always worked out great for me to prevent spun bearings. Coolant + bearings = bad.
I personally use 2 quarts of oil when cleaning out the lifter valley, oil is cheap, a motor + my time and labor ain't. Do this and you shouldn't have any problems at all.
Good luck....
