What is the reason that pre- heated water cannot be used to wash on Shabbat?
Shalom, Thank you for your question. The Rabbis enacted a restriction of washing the entire body on Shabbat with hot water even if it was heated up before Shabbat. The reason for this was to stop sinners heating water up on Shabbat itself - which is a major sin of cooking – and claiming that they had heated it up before the Shabbat day. Therefor they forbade bathing in hot water on Shabat altogether no matter that the water was pre-heated and not a violation of Shabbat. None the less they did allow washing one's face hands and feat with pre-heated hot water. This leniency was left allowed so as to allow people to honor the Shabbat with the minimal hygiene of washing their face etc. This is understood as applying to any small part of the body, as long as it is only the minority of the body. Based on this, one could, for example, use hot water from their Shabbat urn to wash their face or hands, or even their underarms if they wanted to. Blessings.