Regarding Yom Tov, the Torah states (Shemot 12:16) that although labor is forbidden, those acts which are involved in preparing food are permitted. The Gemara learns from this verse that not only is food preparation allowed, but also other acts from which one derives pleasure.
The Ba’al HaTanya (Shuhan Aruch Harav) explains that the Torah used the example of food since this is the quintessential form of pleasure, but that anything else which is universally accepted as pleasure is also permitted. As such, even though using fire is normally a biblically-proscribed act, since it is used in the preparation of food, it is permitted on Yom Tov. Therefore, strictly from the Torah’s point of view, lighting a fire on Yom Tov would theoretically be permitted. Nevertheless, our Sages instituted a prohibition against starting a fire (“Nolad”), since this may lead to one using the flame for something that could have been prepared before the holiday, or for other uses which are not permitted on the holiday. Lighting a flame anew is never permitted on Yom Tov even if it is for a pleasurable act, although one is permitted to light from an existing flame and to transfer it elsewhere, or to increase an existing flame.
One practical application of this law is the use use of hot water on Yom Tov. Many homes have a boiler which heats up water, and when hot water is used, it draws in more water and heats it up for future use. Since the boiler works continuously, hot water may be used on Yom Tov for an accepted pleasure or benefit, such as washing dishes. However, some homes nowadays use what are known as tank-less heaters. This works by starting a flame or element as soon as the hot water faucet is turned on, which heats up a reservoir of water, and within a short period of time, hot water comes out of the tap. This is advantageous because it is energy efficient, but since turning on the hot water faucet necessarily entails the act ofNolad, it would not be permitted on Yom Tov. If an accessory could be attached which sporadically turns on the element to heat the water and that one’s turning on the faucet is not directly responsible for the hot water which flows out, then it would be permitted. Furthermore, when one needs hot water for a Yom Tov use, it would be permissible to ask a non-Jew to turn on a the hot water faucet of a tankless heater system. This is because Nolad and asking a non-Jew to perform a forbidden act are both Rabbinically-instituted prohibitions, and we do not compound such prohibitions.
Summary: One may use hot water on Yom Tov for accepted purposes like washing dishes or washing one’s face. One may not use a tank-less heater system on Yom Tov.