We have noticed that when the bathroom vent is on, and the door is closed, the vent struggles to get air, unless the window is open. It creates what amounts to negative pressure in the bathroom. You can open the bathroom door and hear the fan relax. By the same thinking, or reverse scenario, when the heat is on, it must create a positive pressure in the bathroom. As the air will take the path of least resistance, it will flow out the two vents in the main cabin (if those vents are open), and that is where the thermostat is too, the bathroom will stay noticeably cooler. This is especially true if the door is closed.
So, what we did, is cut a 3 1/2" hole up high in the wall between the two rooms. We cut it up high so no shower water should show up there. Without the furnace running there was no airflow through the hole. When the furnace came on, the airflow through there would almost blow the candle flame out. We put an adjustable SS vent cover over the hole in both sides so the the airflow could be restricted from either side, if ever needed. It will let the airflow coming into the bathroom have a path back to the furnace return vent. The easy way of course is to leave the bathroom door open, but that is an inconvenience when we are sitting at the dinette. I have pictures but this new device is hiding its secret on how to release them.
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