voltage doesnt indicate "heating power"; Watts do.
and since "amps" is the rating that dictates how large your wiring must be (and larger = more expensive), its in your interest to use the highest voltage available which in turn minimizes the number of amps needed.
for example say it takes 500 watts to heat your water bath to the temp you want.
a 500watt 120v heater will take one hour to do that, and will require 4.1 amps for one hour (which is negligable, all household wiring will support 4 amps). to get the same performance out of a 12v heater, the circuit would need to handle
41 amps for an hour. 41 amps requires 6 gauge wiring, and similarly rated plugs fuses, and connectors..... and then you need a 12v power supply that will output 41 amps.
you
can use 120v heaters on 12v circuits, you just have to do the math. a 2000w 120v rated element would output only 20w of power at 12v. there is no reason to hamstring yourself by using only 12v.
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Also If u are using a pid just manually turn down output to the element save money and still maintain slow temp changes

slower output will ultimately cost you more. heat loss is a function of time. the longer it goes on, the more is lost. delaying reaching your goal will only cost you more money (though saving money isnt the intention here)