There are very few mechanical thermostats which can work that close in
differential. The only one I can recall used a mercury thermometer with
leads embedded in the glass tube at the desired temperature.

Even a design with electronics needs careful design to get that close of a
differential. However I wonder if the spec. needs to be that accurate since
this appears to be an anti freeze system.




The Dallas sensors I refer to have a straight digital output so there's
no fiddly analog design to deal with. Still, that is quite a tight range.

If he provides some more detail about the intended application it will
be easier to give suggestions.