The beer is not pasteurized (I assume), so the rules are slightly different. In general, it will "go bad" faster if its warm and the warmer it is, the worse it is. With that being said, its not a fast process by any means. If its room temp, it should still last a few months if its a lighter beer or many months if its higher ABV. Don't let it get above room temp and it should last you "long enough".
The bigger issue in my mind with bottling from a keg is oxygen exposure. If you use a beer gun properly, you probably minimized it, so that's good. In my experience of bottling from kegs, they NEVER last as long as direct bottling. Between oxygen exposure and loss of pressure (there's always some), they always start tasting less fresh sooner.