Hi Filip.
I uploaded my design to OSHPark just to see if it was ok even though my gerbers look ok in Gerbv. I note they are quite a bit more expensive but they do nice make boards.
The IRL6342 looks to be a good choice for TEC switch. Though I cannot see any gate resistor or gate bleed resistor to gnd? Look it shouldn't matter as it's driven from the ATMEGA328 out but its just good practice to include such resistors to lower stray capacitance, improve switching time and help dampen any oscillations.
But in reality if the PWM is 1Hz....I don't think its going to be an issue.
I actually tried permutations of switching our FET without gate resistors...there was no change to conductance nor package Pd. So take the above 2cents advice with the worth of a
grain of salt!
Keep us up to date. Good to see others and their ideas coming together.