John - You're correct regarding thermostat location, but I wasn't taking any chances with the new-to-me boat. My last boat did not have a heat exchanger and was raw water cooled . . . this stubborn old dog can't be taught new tricks I suppose.
I neglected to mention that the real reason for running the engine to normal operating temp, was to fully warm the oil for draining and replacement with fresh oil. I prefer to do this during layup to eliminate most of the sulphuric acid, formed from the sulphur which is present in oil and in the diesel exhaust . . . not especially good for your engine.
Of course, engine pencil zinc anodes are also changed along with oil and fuel primary/secondary filters - naturally, before filling the crankcase with new oil. Biocide added to fuel tanks, electrical connections cleaned and sprayed, battery electrolyte topped off . . . etc.
But now I'm wandering into other boat winterization topics - perhaps more info than the OP asked for.
True Blue . . .
sold the Nauticat