Hi ! Welcome to IRV2! We're sure glad you joined the gang!
Yes, a generator that operates off the main fuel tank will shut down when the level gets down to about 1/4 tank.
Thermostats can cause lots of problems. Hard to say if it would do that. You might want to do a factory reset and see if that helps.
Noticed you are kind of new on IRV2 and wanted to say hello! Have fun and keep her between the ditches!
Good luck, happy trails, and God bless!
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Joe & Annette
Sometimes I sits and thinks, sometimes I just sits.....
2002 Monaco Windsor 40PBT, 2013 Honda CRV AWD