Does setting the thermostat correctly save money?
Modern controllers have solid state electronic sensors that sense the water temperature. They also have advanced electronics and logic that do a very good job of forecasting the required change in temperature. This keeps the heating / cooling from drastically overshooting the set point.
Overshooting the set point wastes a great deal of energy and it is one of the disadvantages to less sophisticated controllers.
The SpaNet SV and SV mini-series have thermal tuning and this is a perfect example of advanced thermostat and controller that reduces energy consumption by up to 15% when using the thermal tuning.