The Gemara (Shabbat 25b) states that there is a Mitzvah to bathe in warm water in honor of Shabbat. The Gemara there writes that his students would bring Rabbi Yehuda bar Il’ai a barrel of warm water of Erev Shabbat and he would wash his face, hands, and feet from it and then put on his Shabbat clothes and would resemble an angel of Hashem.
Indeed, the Midrash (Vayikra Rabba 34:3) explains that the verse “A kindly man benefits himself” refers to Hillel the Elder who told his students before departing from them that “he was going to do a Mitzvah” after which he went to bathe in the bathhouse. The students asked him, “Is this really a Mitzvah?” He replied, “Certainly it is, for the cleaner who is hired to wash and polish the statue of the king that stands in their gathering places is paid by the king for his services. I, who was created in the image of Hashem, how much more so will I be rewarded!” Rav Achai Gaon writes in his She’iltot that this story occurred on Erev Shabbat, and it was therefore a special Mitzvah to bathe in honor of Shabbat.
Thus, the great Rishonim (quoted by Chazon Ovadia- Shabbat, Vol.1, p. 25) write that it is a Mitzvah to bathe and change into clean, nice clothes on Erev Shabbat, in honor of Shabbat.
The Rambam (Ch. 30 of Hilchot Shabbat) writes: “What is honoring Shabbat? This refers to what our Sages said that there is a Mitzvah to wash one’s face, hands, and feet in warm water on Erev Shabbat and then get dressed in fine clothing and await greeting the Shabbat.”
The Mishnah Berurah (Ch. 260) adds that even a Torah scholar whose Torah is his trade must stop pause learning on Erev Shabbat in order to fulfill this Mitzvah of bathing in warm water.
This was indeed the custom of Maran zt”l and he would take a hot shower on Erev Shabbat and change into nice Shabbat clothes although he would never waste time from his Torah study.
When Maran zt”l was younger, he would often go study Torah in local synagogues on Fridays from Shacharit until shortly before Shabbat (He once exclaimed that he would take a banana with him, so he had something to eat.) Once, he went to study in the women’s section of the Shoshanim Le’David synagogue in Jerusalem on a Friday morning with his childhood friend, Hagaon Harav Ben Zion Abba Shaul zt”l. Later that afternoon as Shabbat was impending, Rav Ben Zion told Maran zt”l that the hour was late and they had to stop in order to go bathe in honor of Shabbat. Maran zt”l, however, was extremely preoccupied with his learning and replied that he would follow “in a few minutes.” Maran did not realize that Shabbat had finally begun and continued learning. He eventually became so exhausted that he fell asleep.
The congregation arrived in the synagogue and prayed Kabbalat Shabbat and Arvit, however, Maran did not hear them at all. Later that night, after everyone had left, Maran zt”l awoke, startled, and when he saw that he was still wearing weekday clothes, he had realized what had happened. Unfortunately, he also realized he was locked in the synagogue, and he started banging loudly on the doors until some passersby called the caretakers of the synagogue to let him out. Rav Ben Zion would often recount this story to make a point of how unique Maran zt”l was in his intense engrossment in Torah such that he did not pay attention to other things around him other than his learning.
Summary: There is a Mitzvah to bathe in warm water on Friday in honor of Shabbat. There is likewise a Mitzvah to wear nice, clean clothing in honor of Shabbat. These Mitzvot apply even to those who toil in Torah all the time.
