A toekick vent with screen might work, it lets the air out under the cabinet.

Thanks for this. I should have mentioned that the heat comes from a 9 inch high wall radiator so we think the heat needs to come out from higher than a toe kick would allow.

In that case a vent at the top seems like a good idea since heat rises. How hot does the radiator get? Heat from our toaster hasn't bothered our cabinets but there is no direct contact. Hopefully there is a gap between your radiator and cabinet back.

The placement on which wall makes a difference, behind or beside the vanity. "Filler" usually means beside (because behind you'd have counter depth issues), and the width of filler matters. Also whether it is baseboard radiator heat or an in-wall unit.

The problem here with radiated heat is you need adequate clearance for airflow. The toekick method is good for forced air, not for a radiator far away from the front of vanity.

A picture would really help.

You really don’t want to trap a heat vent inside a vanity — it overheats the cabinet and also blocks airflow to the room.

Best fix is to redirect the duct, not vent the cabinet. If possible, extend the duct and add a toe-kick or side grille so the heat blows into the bathroom properly.

Just adding holes/vents in the vanity will still waste heat and can dry/warp the cabinet over time.

If moving the duct isn’t doable, a toe-kick vent kit or small floor/wall register through the cabinet base is the cleanest solution.