At the Macs here, the burgers are being taken as they are cooked, so are warm. They cool, of course, when one adds the stuff that goes with it.
Beef should never be cooked 'well-done'. Cooking till the 'pink' just disappears is allowable.

Uncooked ground beef, well-seasoned (see as done in Milwaukee, above), is what we called steak tartare, and was a favorite of mine at a German beer garden in Austin, Texas.
Food police don't seem to approve of the good things in life, such as food worth eating.