I know this is an old question, but the Shelly H&T has a USB power cap that you can buy separately. Then use any micro USB cable and power supply. It's Wi-Fi and not zigbee, and it is definitely a tad more expensive per unit. However, no need to worry about batteries. Shelly does run sales occasionally too.
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That was the first one I tried. Sounded fantastic in theory, didn't work out for shit. For some reason the sensor dropped out constantly. The USB PSU bottom was nice though, no batteries to change.
I do find that they go to sleep fairly often. I changed the temp update setting to the smallest value and it updates fairly regularly. If the temp doesn't change much I don't think you get an update.