If your loved one is not able to manage controlling the thermostat, then you have to rely on the caretakers to do so. Generally speaking, they will do a good job --- but not always. I went to see my mother every single afternoon and occasionally found the temperature to be awful. So, I put a large digital display thermometer in her room. I taped over the display face so that you could only read the room temperature. Then I put up a big big sign stating the desired temperature range for all to see. Then when I called her in the evening and in the morning, I'd ask her to tell me what the digital number was. If necessary, I'd call the assisted living desk and advise them of the situation.
Once again, the usual problem with the caretakers was that they were new and unfamiliar. Assisted living facilities have a hard time retaining their better employees. And then there's the assisted living management's inexplicable tendency to rotate the caretakers. Thus, too many things "fall between the cracks", especially in the larger facilities.
Note: Level of spending is no assurance of increased quality of care. Smaller facilities that are on a single floor level are your best bet overall. And daily visits are most helpful.