A trip to the hardware store and a couple of youtube videos had me sealing the gaps myself with fiberglass tape and mastic. Nasty stuff, that mastic.
But now look:
It doesn't make sense to heat the whole house when just one of us works from home in a single room and after a little research we found a solution in a ceramic wall heater. Looking forward to seeing how well it lives up to its claims. Heat at a lower price? Sold.
We will paint it to match the wall soon (isn't it cool you can do that?), but tonight I'm too tired!