Once beef is cooked, the rules shift, but the 40°F line still applies. Cool your leftovers within 2 hours (1 hour if the room is over 90°F, like a summer cookout). Pop them into shallow containers to speed up cooling—no one wants a lukewarm brisket trying to become a coliform breeding ground.
Pro tip: slice or shred large roasts before refrigerating. It’s the equivalent of giving your leftovers a fast lane to safety. And never stack a hot container in the fridge; it’ll warm up everything around it. Let it cool a bit first, but don’t let it sit out too long.