12V 4amp is alot ...are you sure your PSU is capable of supplying 12V at that amperage.
You said it only draws 10.2V? The peltier won't draw that voltage it will draw a current, aka around 4amps at "12V supplied".... This is indicating the PSU you are using is "loading down" and not capable of supplying 12V at 4 amps.
I suspect the peltier is a 48W device thus if you provide 20V it should draw around (p=EI thus I =P/E thus I = 48/20 = 2.4amps). You can vary the E and I proportionally to each other but it will still be a 48Watt device. Thus you original PSU is probably not up to the task.
Do you have another high amperage 12V PSU?
Maybe try the peltier on a car battery! Do you have a 10amp multimeter to measure the I draw?
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