Depends on the gun, the ammo and what you are using it for. If I were looking for the best possible groups and shooting for score or competition I would most likely foul and warm the barrel up before getting serious about my shooting.

However all my hunting guns are sighted in to be on with the first shot out of a cold clean barrel. This takes some time in some cases, but that is the one that counts for me, that first shot. Normally things don't change that much after a few shots anyway. For deer hunting I almost always going to fire one shot, and that is it. And it is after sitting in a stand or blind for hours or days in not the greatest conditions. And my muzzle loader doesn't even go in the house during the season. I load it and it stays outside loaded (with no primer) until I shoot something. I don't much care what it will do after 5 or 6 or shots on a hot August day. What I care about is that first bullet is going to go where I need it to at the ranges I want to use it at out of a cold clean barrel.

I think the only exception would be varmint hunting when precision is needed and you may be taking multiple shots all day long.

You really need to check your gun and see how far off the shots are with the barrel cleaned and after a few rounds have gone through it. Most of my guns don't change much if any.

Paul