MOSFET gets hot when PWMing car high beams as DRL lights
The problem is that you need to give the MOSFET gate a voltage that is positive by 10V or so wrt the source to have it turn fully on. Your MOSFET is connected as a source follower so it will drop probably 5 or 6 volts when it is turned on, which translates into a LOT of heat loss. 

You could try adding this circuit, which AC-couples the gate drive so that it's always positive wrt the source. 







simulate this circuit &ndash; Schematic created using CircuitLab

It's still pretty hard on the MOSFET when it switches off (especially) and on at the beginning and end of the PWM (the MOSFET can dissipate up to 30W or so for a brief time) but it might be okay with a relatively rugged MOSFET. 

Alternatively, simply swap the N-channel MOSFET out for a similar P-channel MOSFET (which reverses the gate drive 'logic' - low = ON). 

You might want to hang a fat TVS across this whole thing.. 1500W type or more.. it might save the MOSFET gate and 555 when transients happen (eg. when jump starting the vehicle).