Q. Is there basis for being able to use hot water for showering on Yom Tov because in today’s times when people have the luxury of having hot showers in their homes it seems to have become much more “shave lkol nefesh”?

A. The Mishna (Beitza 2: 5) records Beis Shamai’s opinion that one may only heat up water for washing one’s feet and only to a temperature that one would be able to drink, while Beis Hillel permit heating up the water even as hot as needed to bathe. Shulchan Aruch 511:2 rules that one may heat water only to wash face, hands and feet, but not the complete body, even when not washed at the same time. Mishna Berura (ibid. 10) quotes Tosafos opinion that this is due to the prohibition of performing melachos that not everyone does or needs (shave lekol nefesh). Although the Shulchan Aruch permits to wash on water heated before Yom Tov, Rema (ibid.) prohibits.
Mishna Berura (551: 9 -18) rules like the Rema, that one may not take a full body shower with hot water on Yom Tov even if it was heated before Yom Tov. However, one may wash one’s whole body part by part with water heated before Yom Tov and one may heat up water on Yom Tov to wash one’s hands, feet, and face.
Shemiras Shabbos Kehilchoso (14: 7) discusses the topic at length and although he maintains that there is some grounds to be lenient, nonetheless he remains stringent. So is Tzitz Eliezer (6: 20, 11: 64), Avnei Yoshfe (3: 55) quoting Horav Elyashiv zt”l, Horav Yisroel Belsky zt”l (quoted in Halachically Speaking), Rivevos Ephraim (16: 265, 8: 248: 1) and others.
Halacha Yomit mentions that Maran Harav Ovadia Yosef Shlit”a maintains (for Sephardim) that if the water was heated well before the onset of Yom Tov and the boiler’s operation on Yom Tov serves only to retain the water’s heat but not to reheat it, one may use this water to wash his entire body on Yom Tov.
Horav Shlomo Miller’s Shlit’a opinion is to be stringent following the Poskim mentioned above. If one usually uses the shower as tisha kavim (instead of immersing in a mikva) the Rov’s opinion is that he may use a lukewarm shower for tisha kavim. Same would apply to one suffering significantly from excessive heat and perspiration on a hot Yom Tov day. A hand shower is also recommended.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a