Re: How to cool bathroom containing furnace?
I'm confused. In the bathroom or in a closet/space adjacent to it?
Sounds like an unfortunate but typical poor quality installation. No branches should be within 3-4' from the plenum. And a bathroom should have a relatively small branch since it's a small space. The amount of airflow for any room should match the heat loss or gain of the room. So a small 100 sqft bathroom located in a basement probably only needs a small 4" branch supplying around 50CFM.
If it's locted in the bathroom, that shoulnt be an issue unless you have air leaks on the supply and return plenum. It sounds like you do. I'd have a professional come out and use foil tape and/or mastic and seal up the leaks. IF there's a supply register, I'd have the closed or even covered permenantly.
You might consider adding a wall or seperating hte furnace some way. BUT... it needs to have adequate airlfow if it's a 80% furnace that needs natural draft.
Finally, to make matters worse, I'd be willing to bet that the furnace is oversized and/or the ductwork is undersized. THis makes any air leaks, leak worse and makes the air that leaks muh, much hotter.
Remember, you're paying for all that heat, you don;t want to just open a window or vent it outside.
1925 Two-Story Stucco Beaux Arts Neoclassical