Thanks for the reply!
Wow I am surprised to hear that! I always thought that at the maximum power dissipation level the MOSFET would just get kind of warm or something, I didn't realize what an extreme case that was. 
The load will likely be intermittent for a number of the wires, but really I would just rather not worry about anything overheating.
It seems to me that a lot of MOSFETs have a Vgs of 20V. How do people control these with the Arduino? I have been trying to to Google this, but most of the tutorials seem to just apply 5V and not worry about the on-resistance.
Thanks again!