I was advised to use an N-channel MOSFET. To find out how hot it will get, I need three pieces of information: the internal on-resistance, the thermal resistance, and the load current.
I am currently looking at the AUIRFB8409 in a TO-220 package, which has an internal on-resistance of just 1.3 mΩ.
http://www.mouser.com/ProductDetail/Infineon/AUIRFB8409/?qs=%2fha2pyFaduggMyepHC84Hkvb6gCj7GkTsVwFtS9Tyg4noEfhEQ3IYw%3d%3d
The TO-220 package, with no heat sink, has a thermal resistance of 62.5°C/W.
To be paranoid, I'll calculate the temperature at 48 A continuous. My stryfe has 2 hellcat motors, and their stall current is 24 A each. At 48 A, this MOSFET will generate 3 W of heat.
With no heat sink, 3 W will make the transistor 187.5°C warmer than the surrounding air. If the surrounding air (inside the blaster) is 30°C, then the transistor will heat up to 217.5°C. Not surprisingly, it will burn out at this temperture. In other words, if the flywheels are completely jammed, and I hold the trigger anyway, then the transistor will burn out.
Realistically, I'm only drawing 48 A momentarily when I start the motors, so the transistor will not get as hot as my calculation would suggest. To calculate how hot, I would need to know how long is "momentarily" and I would need the thermal mass of the transistor. Alternatively, I could just test it and find out.
Finally, MOSFETs can be safely operated in parallel, and parallel configurations are regularly used in power supplies to produce higher output current. Sticking with my paranoid scenario of 48 A, I could use two MOSFETs in parallel. If they're perfectly balanced, each one would generate 0.75 W of heat and become 47°C warmer than the surrounding air. The on-resistance of a MOSFET increases as it warm up. After accounting for this fact, the transistors will reach 91°C each, which is well below their burn-out temperature of 175°C. Even if the motors burn out, as long as they don't short out, a parallel pair of transistors would survive.