I don't even need to get the frugal trait. I downloaded a mod a long time ago that lowers the bills to more realistic values. The house my sims own is currently very large and their bills with the thermostat have come up to about 7k - but I don't consider that much since the household has a crap ton of money. But the trait does help.
So far with the thermostat it seems like a nice feature to me. In winter my sims were getting an uncomfortable moodlet complaining that it was cold so I turned the setting to 'warmer' and they would every once in awhile get a nice little +1 to their mood from the central heat.
For summer my sims haven't complained about the heat indoors even if there is a heatwave outside, but I decided to turn on the 'cooler' option anyway and they get the same +1 moodlet, only the description changes to how much they appreciate the cool air of central AC. I think its pretty cool and my bills are fine.
By the way as far as I know you don't need to have your thermostat placed in a particular spot in your home. Just place it anywhere and it works. Mine is all the way at the right end of my house (and the house is huge) and it covers every single room on the lot, including the greenhouse out in the back. There hasn't been a room where they don't have the moodlet. If you have a room that is missing sections of walls then obviously you have a problem there with it not working correctly. It was the most simplest settings too. Warmer, cooler, and off. Depending on the seasons and the weather you pick any of them. Overall I think the thermostat is a nice addition to the game and reminds me a bit of reality.