thermostat to control RS

OK I am looking for some help with a project I am going to be doing soon, basically I am going to be wiring a household digital thermostat to activate and deactivate a remote start. The thermostat has a relay in it that closes when it is set to heat(or cool) and I want to use this to trigger the activation input for a remote start. this way when the temp in the vehicle drops below a certain point it will kick on the RS and the engine will run until the predetermined temp is reached then it will shut down (possibly via NSS wire or something)I figured there has to be some way of doing this but I am not sure how I would convert the signal from the thermostat to activate the RS, and then shut it down when it goes away (this should be easy enough by wiring the ground output from the thermostat to the neutral safety wire) but how can I get a single ground pulse when the thermostat kicks on?

may have found the answer, use the built in relay on the thermostat to put ground on the NSS input wire for the remote start, then use the same ground output with this relay diagram to trigger the activation input wire on the RS. this should turn the engine on when the temp drops below the threshold then turn the engine off once it reaches the programmed temp.   https://www.the12volt.com/relays/page5.asp#ctm