Forget peltier.

What are you going to do with the extra heat that peltier will generate? You obviously will need a massive heatsink with fans to get rid of that heat, outside of your case. You can't do that within your enclosure for obvious reasons. Too complicated, too expensive, bad efficiency.

Things are simple. Do not complicate it.

Use either something like the above power supply of a reputable brand, or use bigger aluminum heatsinks. Or design your own SMPS for better control of the quality of the design.

Ioannis