The regulator on the Arduino is getting hot with 12V.
A car is only 12V when parked.
With the engine running, it can be as high as 14.5V.
Remember the power taken up by the regulator it the square
of the voltage across it.
12-5 = 7 7 squared is 49
14.5-5 = 9.5 9.5 squared is 90.5
the ratio is 90.5/49 = 1.84 or almost twice the power being dissipated.
It is advised to use an external regulator to take it to 7 to 9 volts
first.
Dwight