Can one use hot water from the tap to wash one’s dirty dishes with on yom tov?
It depends. If, as in Israel, the hot water is coming from a Dud Shemesh – a solar water heater – one may use it on Yom Tov.
If, however, the hot water comes from a boiler, there may be a problem. Although one may use an existing flame to heat up water on Yom Tov, one may not ignite a flame on Yom Tov, nor extinguish a flame. If, by turning on the hot water tap, this causes the themostat to turn on a flame (and/or causes the thermostat to turn off the flame when the tap is closed) one may not turn on the hot water tap on Yom Tov.
If the water is required for a young child or ill person, there may be room for leniency if the ignition and extinguishing is indirectly caused. In such circumstances, one should refer the details of the hot water system to a Rabbi for a ruling.