Update: this morning the manager offered to move us to a room in the 7th floor. Apparently those rooms have air-conditioning even during winter. It does not exactly fix the issue with the random temperature in the room, but at least now I can set the temperature to 21°C. I hope it stays like that.
This room is bigger than the other one, and the bathroom is huge, with marble floor. It's not a suite, but it has a big balcony. There's a large dressing area where the closet and safe are. The room and bathroom don't seem to have been redone lately, there are some signs of wear. But the overall appearance is great, and it looks cozy after all.
The manager had a great attitude in the end (better than the reception lady agent the night before), and did what was possible to fix the issue. He even gave me a bottle of wine as a courtesy. Nice touch.