I am making an electrical fridge for a school project. I am using a 12v Peltier cooler and using a 12v 30a power supply. I have all the wiring and everything already set up, and no matter what I cannot afford to have the Peltier burn out or anything even though I had one burn out before using the exact same setup and wiring, though that was a smaller model still 12v, but the Peltier isn't working at the cooling power that its supposed to be. it cools down the fridge to 68° f when it should be cooling to 20°f, and I think it might not be getting the power it needs, but the wires that I'm using are extremely small, like 22 gauge, but I have them doubled up, one concern I have is that the input and output wires for the Peltier warm up a lot, but not enough to melt the wires, even though it melted the wires for the first Peltier that burnt out. The reason I'm going into such detail is that I know basically nothing about electrical things like that and want to know if the context matters and I really need to know what the warm wires are because of, and more importantly if it would be safe to use thicker wire.
Update: I do have a lot of cooling on the hot side, I have a CPU cooler meant for a computer on the hot side, so there isn't a problem with that, but the first time that the Peltier burnt out it didn't have any cooling at all and was extremely hot. Also, I am also wondering if a wire too thick would damage or cause the Peltier to burn out? Like I said before, I can not afford no matter what fo have that Peltier burn out.
Also, my power supply's input is 115 or 230 but I keep it on 115 because I don't want the thing to burn out just in case that matters