FigZ:
Nice - thanks for sharing
what exactly do the relays hook up to and what do they do?
This could be different for a lot of heating systems, and it is the core of your whole idea.
With one relay you can switch between your current thermostat and the arduino thermostat.
The second thermostat turns on / off your heating system the same way your current thermostat does.
I uploaded some simple schematict in the opening post.