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Problem would be power dropped over potentiometer. I draw Peltier ~ 2.5amp I (nominal), your lower Peltier voltage from 12V to lets say to 5V. of course you lower Peltier voltage it's I draw will change as well.
Thus that this stage we have 7V dropped across pot. Power across pot P = EI, P = 7 x 2.5 = 17.5 watts energy dissipated thru pot...a lot.
This is why proportional voltage control is difficult.....if you used a transistor to lower the voltage you would have similar power drop across it.
This is probably why devices control is done with PWM...changing mark space ratio, driving a FET and Peltier.
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