How do I help the caregivers with my mother-in-law's temperature issues?

My MIL, aged 93, is suffering from dementia. I believe she is in stage 2 of 5. She has 2 caregivers that alternate looking after her. They are with her 24/7 for one week, then the other caregiver comes in 24/7 for the next week, etc. My MIL will crank up the heat to 85 degrees because "she's cold". We've asked her to put on her a sweater and some warm socks, but she's refuses to saying "it's my house". She wears short sleeved tops and nylons, even during the winter. The caregiver find it very, very uncomfortable and many times have to go to their bedroom, close the door and open the window to get some relief. They are there to watch her, not spend time in the bedroom, but I understand why they do it. I know when my husband and I come to visit the minute we walk in the door we're blasted by the heat. We just recently got ahold of a friend in the HVAC business and he went over on the pretense of checking out her furnace before winter comes. He's changed out the thermostat so that it won't go above 75 degrees, regardless of what the display shows. Well, that very same day she called complaining that she's turned up the thermostat and the furnace won't come on and that's she cold. She also called the next day and the following day complaining that she wants this fellow out again to fix the furnace. We told her we'll be coming by next week and she'll have to wait until then. We've also reminded her that she could put on a sweater and socks. We don't know what to do now. Any suggestions?