The Hachamim instituted restrictions regarding bathing on Yom Tob. It is permitted to wash one’s hands, face and feet, even if the hot water was heated on Yom Tob. This means that it is permitted to turn on the hot water faucet, even though this causes more cold water to be heated by the boiler. This is a leniency does not apply to Shabbat.
However, the Hachamim did not permit heating water on Yom Tob for taking a full-body shower. Moreover, the Rabbis instituted a Gezerah (precautionary enactment) prohibiting bathing even with water heated before Yom Tob. This restriction is known as "Gezerat Merhasaot" and was designed to prevent bathhouses from heating water and operating on Yom Tob, with the excuse that the water was heated before Yom Tob.
This Gezerah only applies to bathhouses, and therefore in a private home, technically one could take a shower with hot water heated before Yom Tob. The problem is that when one turns on the hot water faucet, cold water enters the boiler and becomes heated on Yom Tob. Hacham Ovadia rules that this is not a problem. Ideally, the problem can be circumvented by having a non-Jew turn on the faucet. There is no problem of Amira L’Akum (instructing a non-Jew) to perform a "Pesik Resheh." Alternatively, there is no problem bathing in lukewarm water, no higher than body temperature. Hacham Bension also concurs with this.
SUMMARY:
It is permitted to turn on the hot water faucet on Yom Tob to wash one’s hands, face or feet. One may not heat water on Yom Tob to take a full-body shower. There are circumstances under which one may take a shower using water heated before Yom Tob.
