Keep the 40A seperated from the Arduino, that is good.The Arduino can not drive such a relay. You need a mosfet, a resistor (or two) and a flyback diode.Or use the 40A power supply also for the relay, but use an opto-coupler for the relay (the mosfet is still needed).Do you know how to calculate the temperature ?https://learn.adafruit.com/thermistor/
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