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"can peltier coolers just accept as much output as they are given like a water heater element?"
A water heater element, a resistance heater, actually increases in resistance as it gets hotter, and will burn out like a fuse if you apply too much power to it, exceeding the wattage rating of the element by jacking up the voltage.
I'd expect the peltier device to burn out way faster. A 12v rated peltier may have a maximum voltage rating of 16V and a power rating of 80W. Exceed either, and it becomes toast. In a nominal 12v system you need to ensure it can run safely at 14.4 volts (alternator power) and that it will never see more than 16V or whatver the max rating is.
If you use solar cells with a 17-22V maximum output, you've got expensive toast. If you use a drop regulator to reduce them to under 16V output, you may be throwing out 1/3 of your power before it goes past the regulator.
Gensets use "dump regulators", conventional solar regulators are "drop" regulators, just like the 3-pin single chip 317s and 7812's sold in electronic stores. (Which typically convert excess power to heat in their heat sinks.) Alternators are entirely differently, they regulate their output by cutting back their input and actually producing less power--instead of throwing it out.