Really the Tstat just controls the operating temperature of the engine. The Thermostat shuts down the flow of coolant through the engine until the coolant reaches the thermostat's rated temperature. It doesn't just "click" open 100% so it is an approximation, and the rated temperature is typically the point at which it is fully open. The heat works better because the engine is running hotter and the coolant flowing through the heater coil is hotter. It shouldn't affect the A/C at all though.

The big thing is that a diesel's combustion is by the heat and pressure created inside the cylinder. The hotter the engine is, the easier it is to make the fuel burn (to a point). Additionally the PCM adjusts the injection timing advance based upon EOT (engine oil temperature). Supposedly it starts advancing the timing around 185* EOT, and goes up from there. So really the engine isn't starting to run to its full potential until the PCM sees it is at optimal temperature. Besides, International installed 203* Tstats in all the DT444E's that they produced for medium duty use, so the engine was originally designed to run best at that temperature.