hooked up to the cold water. the machine heats the water itself.
dishwashers are designed to heat warm water to the ideal washing temperature. your home water heater is likely -depending on its age, of course- more efficient.
can a dishwasher heat cold water to washing temperature? yes.
is it the most energy efficient way? not necessarily. and depending on the model the heater may be on a timer not a thermostat.
is this a life or death situation? no. less than ideal? depending on the model, quite possibly.
given that the vast majority of water heaters today are still the standard electrical type, the energy required for a brand new standard electric water heater 