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Our whole dining room extension thing (brick built, proper roof, semi glazed walls) has been completely off limits for all of December and the last ten days or so. The floor takes all the heat out of the pipes before they can reach the far radiators. 30sq/m of house, lost. I despise it. Thankfully has a door into the house, so we've airlocked it off to keep the rest of the ground floor (barely) warm.
I would worry about ground floor temps with this kind of structure with the doors taken out. I've posted in the home-owning thread previously about our kitchen conservatory, which is a similar setup, and does not perform well (we pretty much abandon the kitchen table for winter because it's so cold in there).
https://www.aliceinscandiland.com/blog/2017/03/12/how-to-extend-your-home-with-style-for-less-than-you-might-think