replace fireplace switch with nest thermostat

I have a fireplace wired up to a switch (simple off/on), and I want to throw a Nest thermostat on there.

It has a black and white wire coming out of the wall. I think the white goes to the W1 and the black goes to the RH?

I may have to run a common wire as well I read.

But is there any risk replacing the switch? Do I have my hook up correct?