Why does Arduino get damaged when used in this relay circuit?
The most likely reason is that with a 12 V input, you're overloading the poor 5V regulator IC on your arduino board: even at benign currents, it has to dissipate (12 V - 5 V)•(current) in heat, and that IC is tiny.
Other than that: your heater draws less than an ampere. That's not a big load that you need a relay for; a slightly more generously sized general purpose npn transistor or logic level n-channel MOSFET would totally do, and remove the only &quot;dangerous&quot; part of this circuitry (the flyback voltage of the relay's coil). We can't guess from your description whether you're using an appropriate flyback diode, since you mentioned neither diode nor relay model, but seeing the relay is superfluous, well, get rid of it.