Latching relays are wonderful power miserly switches. Unlike a solid state relay, which requires control current (anywhere typically between .25mA and 20mA depending on what you choose), a latching (mechanical) relay will latch (hence it's name) when pulsed. A short burst of 100mA or so and you are done. If your thermostat is switching the HVAC once an hour per day (which is pretty excessive), then you are still using a lot less power than a solid state relay. Another potential problem with solid state relays is heat. They generate heat. They can overheat and if you don't choose and place your components wisely, they can affect the temperature sensor.
With latching relays, your modern latching thermostat is not consuming that much energy.
Interestingly, I believe that the NEST uses solid state relays.
A quick google shows that some NEST customers are having battery issues. Here is an interesting one:
This is the kind of issue I want to avoid. The two household gadgets that I don't want to think about (battery) power problems are my smoke detectors and my thermostat. I'll check once a year, but beyond that...
Here is a target: Ignore UI and wireless for a moment. Once a temperature schedule has been set, can you design a thermostat that will run for 10 years off of a couple of Lithium AA batteries? That is my starting point.
So, as boring as "Thermostat design" sounds, it poses an interesting power problem. Add sophisticated 'internet-of-things' functionality and now you have two problems.