For local WiFi, anything that's HomeKit compatible should work, but you'll likely lose out on something by restricting its access to the internet. For example,

For local WiFi, anything that's HomeKit compatible should work, but you'll likely lose out on something by restricting its access to the internet. For example, my Ecobee can be controlled locally via Home Assistant (using Home Assistant's HomeKit Controller), but it gets outside weather (used to figure out how early to turn the heat up to meet the schedule requirements) via some cloud service. Plus the HomeKit interface, at least when used in Home Assistant, is not as full-featured as the native (cloud-based) one. If you desire 100% local control, it's worth looking at Zigbee and Z-Wave thermostats. Using Home Assistant can give you full local control without requiring a vendor's hub and app.