A hole like that is unlikely to do much without some means of air flow. If you have forced air heating and the heated room doesn't have its own return, you could create flow by closing the door of the heated room and keeping the door of the unheated room open. Otherwise, I doubt this will accomplish what you think.

Farther down the wall dividing the two rooms, there is indeed a door I leave open. Where I would locate the heat register in Room A is aside a 38,400 BTU Rinnai wall furnace. The Rinnai certainly does heat Room B on the other side of the wall via that open door. All I want with the register is to add a little more. Room B is just a workshop.

I mentioned a forced air system that could blow air out of the warmer room if its normal path to the return were blocked by a closed door. What you have is not that and I doubt your idea for a small through-wall passage will do much if a door between the rooms is already left open.

Yes, that's what you said. But with the 7 stage direct vent Rinnai wall furnace I have, the heat flows everywhere, under doors and other openings. So I see no reason why heat flow to Room B would not be even better. See this video. Rinnai wall furnace heats entire house

What I was aiming at was a pressure differential causing flow. What you have doesn't do that.

Heat does not "flow" through closed doors on its own without airflow. If it did, you wouldn't have this question to ask.

Guess I am not understanding. All I know is that with the same Rinnai wall furnace I have upstairs in the living room, as per the video, heat flows under the closed bedroom doors.