I want to use this thermostat for a propane furnace. No AC involved. It is a 24 V system with three wires. Green wire goes to G on the existing thermostat terminal block. Gray wire goes to W on block and red wire goes to RH. The thermostat that I am using now works fine however I want to be able to monitor house temps. by Wi-Fi app. Also want to set temps up or down using the app. The Nest thermostat has a built in rechargeable lithium ion battery so will it be charged with my present system? Will a "Nest power Connector" need installed?
If you have a c - wire, you can use that, but if none there's the nest power connector. I believe you have the thermostat with 2 triple A batteries on its back. Usually, it's recommended to have a c - wire or nest power connector installed so that your thermostat will work smoothly for the long run. If you don't have the nest power connector or a c - wire, then Google will send you an email notification that you'll need a nest power connector, or while you're installing the nest thermostat and while setting it up from google home app, the app will recommend the nest power connector.