I agree with you about the bench, however, it appears your heat and air condition registers would complicate things. I am sure someone could figure that out. Another idea is to use a pub table in the nook for some fun seating. (Eating, talking, playing games, etc.) Do you have a nice view out the windows?

It will need to be cantilevered and left open above the baseboard heat. That may not be the look you want, but here's a similar example done in a breakfast nook.

A high top pub table with a couple chairs. A glass table top will make the
area more open.

HI --- I think you would regret a built in window seat after a while . The bench you have is the wrong bench . The area is really too small and filling it in with a built in window seat will make the room feel smaller .And the heating is a problem . You could try another style bench , one that has just a padded top with slender more modern legs . Or just do two small cube ottomans or just a big potted parlor palm . Maybe drape panels on each side if possible with that style baseboard heating would dress up that wall .

Thanks for all the comments. My fear is I would regret the built in. Here are two built ins I was thinking. They would let heat out. Maybe not enough.

I don't think you'd regret either one of the benches you show above which are rad covers and would allow the heat to escape from the baseboard heaters. Biggest issue would be removal if something had to be repaired with the heater units. And I'd always be gravitating to the bench to warm my buns in winter! Of course, if fitted to the shape of your bay, you'll need custom designed cushions.

http://www.prettyhandygirl.com/2013/06/building-a-window-seat-with-storage-in-a-bay-window.html

Don't think dyllane's idea will work with the baseboard heater.

Perhaps you don't need to do a built in if you just find a bench that has a lower profile. Look for one without arms because it will feel more natural in the space.

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