Even switched for 100ms every couple of seconds, I'd be employing a gate driver to reduce the switching and to ensure that I gate the gate as close as possible to +5V.
Your circuit will probably switch quite slowly, and the peak power will be very high -- this may not result in failure due to heating, but definitely isn't good for the mosfet.
if switched for 100ms every second, the energy dissipated would be...
0.1 * 2 * 20 + (2.2 E-9 / 0.011) * 50 * 20 = 4J (the extra stuff confirms the switching speed is not an issue)
so we're looking at an average dissipation of 4W.
With no heatsink, the junction temperature (Tj) will reach ta + Tja * 4 degrees C = 25 + 62 * 4 = 25 + 248 = 273C.
The absolute maximum Tj is 175C, so that's a reason why it's smoking. If it smokes even with a heatsink then something else is wrong. Even a 10 degC/W heatsink would keep Tj under 70C, which would be fine (to keep it below 150C, even a 30 degC/W heatsink would suffice (and that's tiny).
To stop it smoking, either a heatsink, or an average dissipation of 2W (or less) is required. This could be achieved (for a 10% duty cycle) with a load drawing less than 15A, assuming you can drive the gate to achieve the rated Rgs of 0.077Ω.
I suspect the other mosfets have an Rds(on) of less than 0.077Ω, or the duty cycle is lower.
A device with Rds(on) of 0.007Ω will have an average dissipation of 280mW -- so it would hardly be warm.