The sooner you clean the casing, the better, as the residue seems to get harder as it cools.
As soon as my casing is cool enough to handle, I take off both closures and set them aside, then I put my thumb on the nozzle and push the whole works out of the casing and into the trash bag. Take a baby wipe and wipe out the threads really good, then the rest of the casing interior, trying to get as much crap out of it as you can. Then, clean off the closures the same way - paying special attention to cleaning the threads. If there's "stuff" I can't clean off with the wipes, I'll use a toothbrush with some vinegar, then wipe it off with a baby wipe again.