You really only need a thermostat that has a on/off relay.
Not sure if it’s available to you but a DHS/ZHS 110 Thermo should do the job.
It’s either 24v or internal battery operated.
See this link (other forum) for a brief discussion.
http://www.smartliving.com.au/forum/viewtopic.php?f=10&t=121
I’m using it in a HVDuctedAC with a twin wires successfully, it should be OK with your fireplace.