SmartThings does have zigbee home automation (ZHA) support as well as zwave, But the most popular thermostats that work with it are Wi-Fi: the Ecobee (Officially supported by smartthings) and nest ( no official support, but there is a community created integration which works well). (There is also a set of paid third-party code from Yves Racine that you can buy for the ecobee which give you all kinds of fancy feature options if you want to use that, some people do, some don’t.)
As it happens, nest is just introducing a new set of remote sensors that we’ve been talking about in the forum, but nobody has them yet we don’t know how well they’re going to work. The range is limited to about 40 feet, which seems short, but again we’ll just have to see.
We have the ecobee at our house and really like it, but different things will work for different people. 
The following is a good recent discussion on different thermostats (This is a clickable link)