If you cover the arch way on each side, you'll trap air in there, which is a better insulator than foam alone.
Looks like a good plan, though.
You could consider a portable IR heater, which only heats whatever the IR is pointed at, to keep you warm while you're sitting in your favorite chair doing whatever.... point it at yourself, and you can mostly forsake the rest of the apartment temps wise, because you'll stay warm. Wear dark clothing, it will absorb more of the IR and you can keep warmer with less energy use.
Try to live away from the windows as much as possible, unless you absolutely have to have the sunlight.
If you want to try a fairly simple experiment, and you have available sunlight during part of the day, hang a coiled up 50 foot garden hose full of water out your window, and run the inlet and outlet of the hose to a small radiator with a fan behind it. It's a quick and dirty solar thermal heater, no pump required.
Neighbors might whine about that one, though.
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