How to wire a relay for an evaporative cooler to a thermostat?
You'll want to connect the Y and C wires to the coil of the relay, so you end up with something like this.



When the temperature switch in the thermostat closes (calling for cool), 24 volts will be applied to the relay coil.This should pull the contact in the relay to the normally open (NO) position, allowing electricity to flow to the evaporative cooler (or whatever 120V device needs to be powered).