Heating up a nichrome wire, MOSFET got too hot
Your heater at 2.4 ohms with 12 V will draw a current of I = V/R = 12/2.4 = 5 A.
While that is within the capability of the MOSFET's 13 A rating, you are failing to account for the power dissipated in the MOSFET itself.
At 5 A and 0.280 ohms RdsON you will get P = I^2*R = 5^2 * 0.280 = 25 * 0.280 = 7 watts.  The datasheet shows a Rthj-amb of 62.5 C/W.
So 7 watts will give you 7 * 62.5 = 437 C! That's WAY too hot. The max operating temperature is 150 C.
You need a heatsink capable of keeping the device below 150 C or you need a different MOSFET that will not dissipate so much heat.