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There should be a register cover on any duct work. Our sig HC 343RL 5er has one in the floor in front of the sink and a second 3 feet away in the bedroom. Installing 8 buck adjustable identically sized register covers from Home Depot was about the first thing I did after the initial long trip upon buying the RV. This allows you to regulate flow. Also, you have the second "problem" in that yhe furnace is directly below the bathroom floor adding to any heat by radiation.
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