Should I install thermostats on all radiators in the room?

I would recommend installing temperature controllers on each radiator in your case. So you can adjust the required temperature for each room separately. This is not a prerequisite, but if the budget allows, it is better to put thermostats in each room. In addition, if you look for offers on radiators in building hypermarkets, many of them offer temperature regulators as a gift. So you can kill two birds with one stone, as they say.