If you don't drive the car home with the heat on, you won't get condensation in the barrel. But, if you do, its better to unload the gun.
Years ago, now, here in Illinois, we had a law that defined a unloaded gun as being unloaded- No powder or ball in the barrel. About 10 years ago, a Hunting regulation was introduced that allowed a MLer to be considered " Unloaded" if there was no powder in the flash pan, or no percussion cap on the nipple. We could then transport guns with loads in the barrel. Before that, we had to remove the charge by either pulling the ball, or by shooting out the load.
If you want to avoid rusting in the barrel while hunting, run a greased cleaning patch down the bore after seating the PRB in the bore over the powder. You can also put a piece of plastic Wrap between the powder and the PRB to seal the barrel from moisture so that it can't get to the powder charge during a long hunt. With a percussion gun, put a piece of plastic wrap over the nipple before seating the percussion cap on it. Then trim the extra plastic off. That will keep moisture from getting into your powder charge through the nipple.
That can and does happen. I hunted all day here on opening day in November, with 5 men who were shooting percussion rifles. It was foggy in the morning when we went out in the dark to our stands. It drizzled a bit that afternoon, and was raining a bit when it grew dark, and we came in from our stands. Because we could not legally transport a gun with a loaded barrel, we all fired off our guns at a damaged tree that had to come down anyway. NONE of the percussion guns fired. The 2 flintlocks fired on the first hammer fall. We loaned priming powder, and I got out my nipple wrench to remove the nipples from some of the rifles, so that we could put 4Fg powder down the flash channels under the nipples. With that done, the guns fired. None of the barrels on the percussion guns showed any water down the muzzle. The owners had all kept the muzzles down during the hunt, and when coming back in to the camp. Many of them were wearing rain ponchos, that covered the stock and action of the guns. The powder could only have been fouled by moisture getting to the main charge through the nipple.
We all learned a lot that afternoon.