First, doesn’t matter ac or dc, it’s a resistance. I personally use 1500 and 1000w 120v water elements. You can derive the resistance, but on 12v they won’t make a lot of heat. I use extra array power out of the inverter After the battery charges to heat a preheater hot water tank and send that to my regular heater which is a propane heated tank. Both are 30 gallon.
Power dissipated by a resistor is V^2/R
if you apply 1/2 the voltage, you get (1/2)^2 = 1/4 times the power.
A "12V" panel puts out about 17V, more or less depending on current draw.
(17V/120V)^2 = 0.02
A 1500W 120V element connected to a "12V" PV panel would put out 1500W x 0.02 = 30W
Make that two "12V" panels in series and you would get 120W. Three in series for 270W (a good load for 3, 100W 12V panels)
The problem with doing this is that the thermostat, also the over-temperature safety switch, are only designed to interrupt AC. They will probably fail on DC. Especially at lower voltage I might be able to implement a "snubber" to stop the contacts from burning. Better would be to wire the thermostat into coil of a relay rated to handle the DC voltage and current, have it control application of PV DC to heating element. With the thermostat switching an inductive load, I would add an RC snubber to prevent arcing and burning of the contacts.
The DC elements with thermostat built in are designed to switch DC reliably.
An easier and safer way to use the water heater as a dump load for excessive PV power is to feed it off your inverter. The thermostat and safety devices built in to the water heater will work reliably then. Either use the water heater at its rated power, or connect a 240V heater to 120V supply for 1/4 the power draw. Many have two elements, so you can use one or both to adjust power draw. If you wire the two elements in series, that will draw half the power of a single element.
Because temperature of water will likely vary depending on surplus PV, you can install a tempering valve to blend hot and cold, delivering constant temperature. Then you can jack the thermostat setting up higher than typical, for more energy storage in the same tank while the tempering valve provides scald protection.
If you don't use a tempering valve, you can at least put a "scald stop" on the shower head. People do receive severe burns from showers when water heater is too hot. I have a shower with tempering valve built in, which was very nice (doesn't go hot when someone flushes), but became gummed up with minerals after many years.