Here's an interesting but very old paper - two theories of Heat Control.
It discusses mental models of home heating systems (thermostats) non-experts use.
These models tend to be extremely wrong from theoretical perspective, but surprisingly useful in practice.
The findings are applicable to a much wider range of subjects than just thermostats, and have certain epistemological significance, especially with regard to compartmentalization.
I take it that by "extremely wrong from a theoretical perspective" you mean that they contradict the more general theories physicists use to explain the universe? Or something like that?
Yes, thermostats are simple on/off devices, with on/off switch based on temperature setting and sensed current temperature ('threshold theory').
Folk theory held by about a third of the public (called "valve theory' in paper) states that they regulate heating in a way linearly proportional to current setting, without any temperature sensing.
Valve theory is trivially demonstrable to be wrong, and yet it has about the same number of successful operational predictions as threshold theory.
It turns out that threshold theory needs a lot of extra complexity until it definitely beats valve theory.