Almost all the energy a washing machine uses goes on one thing: heating the water. The drum, the pumps and the spin draw very little by comparison. That single fact is why turning the temperature down is the easiest laundry saving there is, and why it works without leaving your clothes any less clean.
The heat is the cost
Because heating water dominates a wash's energy use, dropping from a hot wash to a cool one cuts the energy markedly. A thirty-degree wash uses considerably less than a forty or sixty, and a cold wash less still. The mechanical action of the drum and the detergent do most of the actual cleaning; the hot water is largely there out of old habit. Lower the temperature and you keep the cleaning while shedding most of the cost.
Modern detergents are made for it
Today's detergents are formulated to work at low temperatures, with enzymes that lift stains in cool water, so a thirty-degree wash gets everyday laundry perfectly clean. The era when you needed a hot wash to shift normal dirt is long gone. For the bulk of your washing, lightly soiled everyday clothes, low and cool is all it takes.
When to go hotter
There are sensible exceptions. Heavily soiled items, greasy work clothes, and laundry from someone unwell benefit from a hotter wash to deal with bacteria and stubborn grime, and towels and bedding occasionally like a warmer wash to stay fresh. Running an occasional hot maintenance wash also keeps the machine itself clean and free of odour-causing residue. The point is to reserve heat for when it is needed, not to use it by default.
The rest of the laundry savings
Wash full loads rather than half-empty ones, since the machine uses similar energy either way. Use a high spin speed to wring out more water, which shortens any drying that follows. And wherever you can, dry on a line or airer rather than the tumble dryer, which is by far the most expensive part of doing laundry. Together these turn washday into one of the cheaper chores rather than a hidden drain.