I have recently installed an outdoor wood stove with a heat exchanger. The exchanger only works if the fan turns on. I would like to have a thermostat for the fan to turn on without the gas turning on but still have a thermostat to turn the gas on in the event the fire goes out or we decide to go on vacation. Do I have to install a seperater relay for this? Or is there a way to use the existing set up that is there?

This is kind of like having a fan control on your stat for auto and on. Obviously auto is only when the system calls for heat or cool. On is used if you want to circulate the air consistently.

You can achieve what you desire but you will need a separate rely and stat to do so.