You should find a FET with a much lower RDS_on than more current.
not surprisingly these two go hand in hand. One 50A FET will have low Rds_on by design otherwise it will dissipate a lot of power.
The IRF3710 for axample is a Monster with 23mΩ . At 2A you only have 92mW at the FET.
you got this wrong: Rds_on is the FET is fully open, and the FET + resistor are the only components eating the power. There won't be 2 A flowing through there, but much more: 12V / ( 23mΩ+ 0.33Ω ) = 34A
The FET will never get to work in on-off state, it's Rds will never come close to those 23mΩ so it doesn't matter how low it is.
If you want to pull 2A from a 12V supply, you HAVE to drop 24W somewhere. You can choose a huge power resistor(also higher value) and a low Rds_on FET, thus dropping most power on the resistor. Alternatively you can use a lower power resistor (3-5W, but lower value) and a higher power(!) FET and drop more power on the FET. Either way it'll work, but I find FETs cheaper to come by - old ATX PSUs etc.
And this 6A reverse Diode you don't need, most MOSFETs have a build in high current reverse one.
The diode I used is in series with the FET and the power resistor, it's used to protect against reverse connection when the internal diode would be forward biased and subject to the whole power dissipation. It's not paralleled with the FET.
This 0R1 5W resistor is not the best idea. At 2-3A it goes glow. Use 25W or more, like Martin. You feel better then, belive me.
3A on a 0.1Ω dissipates 3*3*0.1=0.9W. What are you talking about?!
The best, you don't need those large heatsinks or PC cooler. You can still use your old one.
as I've said before, you have to dissipate the power somewhere. Either FET or resistor, so cooling stays the same, sorry.