Hot water urn on Shabbat timer

[ralph.lasry]

Showering would still be a problem.

Hot Shower on shabbos

There are two issues with showering on Shabbat. Bishul - heating up or causing water to be heated up. A Rabbinic gezera of bathing on Shabbat. If the boiler is set below Yad Soledet - 130°F then there’s no Bishul problem. If the bathing is not for pleasure (you’re uncomfortable because you’re sweaty…) then there’s no gezera by mitztaer

Shower on Shabbat or Yom Tov

It still would be prohibited. Hot water that was heated up before shabbat can be used for hands and feet but not the entire body at once. A dud Shemesh is considered chama but still prohibited because there is a gezara against full body showers with hot water.