That's not how it actually works though - and is a common misconception. See here for some references from the US DoE and others (easier than putting them here on my phone).
Basically, it's not super inefficient to heat the house back up and being at a higher temp (and increased gradient to outside teml) is harder to maintain and uses more energy overall.
Not OP, but likely. It's suppose to be one of the best ways to make grilled cheese - has to be "real" mayo though, not light or something like that.
Think they dia Scussed it on ATK, Splendid Table or Milk Street Radio.