I think what you want to look at is the iFrame Advanced driver. I have setup a very rudimentary example that loads another HE dashboard, which only includes the thermostat control, which I think may be what you want. I can "pretty it up" in the next few days and show you how it works, if you want.
You could overlay the switch tile that launches the iFrame over the top of a temperature tile, to get the full effect you are after.