For Zigbee thermostats, this should be useful for you:
In the most recent release (2.2.4) of HE, there is a Thermostat Controller app that can be used along with sensors placed around your house to control a Zigbee or Z-Wave thermostat. Along w/the built-in Thermostat Scheduler app you can set up your preferences for heating/cooling, etc. More work for you to set up, but 100% local.
Some screen shots below:
Select Add Built in App button from Apps page, then select the Thermostat Controller and Scheduler to install them.