Its more complicated than that.The voltage produced by a thermocouple is a difference in temperature between the hot and cold junctions, the hot junction is the part that mounts in the exhaust, and the cold junction is where the wires hook up to whatever the are hooked up to(thats not made of the same materials as the thermocouple).So unless the relay is at the exact same temperature as the gauge, there will be an error in temperature, not a huge error, but there is error.There is a temperature sensor inside the gauge(or whatever the thermocouple plugs into) that reads temperature for the cold junction compensation, you'd have to move this sensor to the relay(so it measures the temperature of the relay) for it to be totally accurate.
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