How to digitally control a MOSFET?
A good way to mechanically kill a Peltier is to switch it on and off sufficiently infrequently that it changes temperature, anything longer than a few seconds for instance. Thermal cycling degrades them.

A Peltier shifts heat proportional to the average current, but generates waste heat proportional to the current squared, so even fast PWM gives you a much lower efficiency than steady DC of the correct value. Use a proper buck converter with an output filter for controlling the current rather than simple PWM.

If you compare a linear FET control with buck converter, the overall efficiency will be very low for the linear regulator. In addition, a FET does not make a good linear regulator. Most BJTs, but few FETs, are rated for steady power dissipation. A good way to destroy a typical power FET is to let it dissipate steady power, even when well heatsunk, and well within its headline maximum power.

So, get a design for a buck converter, and build one of those round your controller. Or buy one.