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.
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.
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)