Central Air and Hot Bedroom
Absolutely add a vent above the door's HEIGHT (explained at the end) instead or on the ceiling. If the hallway connects to other rooms, then add vents to them too. This would turn the entire hallway into a return duct of negative pressure &amp; should've been done PROPERLY from the start.

Meaning, the vent should NOT be a hole straight through both sides of the wall. The vent on either side of the wall should be offset from each other by a minimum of 4-feet, for soundproofing or privacy. YOU (being the one stuck with the dilemma) would drill holes through wall studs or the wall's top-plate stud to "connect" the inner &amp; outer vents.