As Ecnerwal says, generally speaking washing machines do not have heaters, but take the hot from the hot water from the hot hose. There are a few European and Korean models that have instant water heaters (which use a lot of current which you may not have) but perhaps due to the massive current demands of instantly heating water, these heaters are often "helper heaters" apparently, for a warm wash, or increase the temperature warm water.
I have not come across word of a washing machine with a non instant water heating method, due perhaps to the problems of having a heating element in the drum with your clothes. Hold on the Frigidaire Affinity has only a 1000W heater. This is low for an instant water heater such as on a shower which tend to have more than 4000 watts to get to typical shower temperatures and pressures. Perhaps the Affinity fills very slowly, or cycles the water through the heater more than once.
In Japan almost everyone washes in cold water, with the exception of those that re-use their bath water while it is still hot. The bath water even if reused, is generally re-used the next morning when it is cold. The Japanese sweat less than Westerners. But if you use a biological washing powder and leave your wash to soak you can have the same effect on organic dirt (such as sweat) as you can in a hot wash, without doing the damage to your clothes that hot washes can do. Hot water tends to damage elastic for instance.
Try a long wash cycle or soak if you have that setting with a biological powder (assuming it does not bring you out in rash :-o ).