What do you think? Worth a try don't you think?
But only if the area to cool/heat is very small. (Like a laser diode).
1-3Amps is way too little for typical cigarette to cigar box large devices.
In other cases the peltier with its heat sinks is way too slow.
It is also highly recommended for protection against overheating.
Even cheap Peltier car cooler boxes use a mechanical thermostat switch.
I would never trust a processor alone.
How will you explain your fire assurance that you have trusted a microcontroller?
I have a different strategy:
use a peltier car cooler box. (50-60W)
Let the cooler run most of the time from 32 deg C down to 10 deg C and up to 15 deg C.
For the rest use simple heater foils 2*12W (with reduced voltage) on a aluminium plate to heat for fast temperature control.
I usually also use 2 temperature sensors: one at the aluminump plate (fast reaction P-controller)
the other at the place of interest to do fine adjustment. (I-controller).
with best regards
Andreas