Bathing on the Eve of Shabbos, when his father is sitting Shiva for his grandfather

If a person's paternal grandfather has passed away, and he is observing some mourning practices until Shabbos, can he take a hot bath in honor of the Shabbos as is his custom?

A person who is accustomed to bathing in hot water every Eve of Shabbos, can bathe in hot water even on this Eve of Shabbos. However, one who is not accustomed to this, should only bathe in lukewarm water that does not clearly feel warm.

Turei Zahav, chapter 374, subsection 2, cites in the name of Sefer Masa'at Binyamin, that one should be stringent, not to wash the head with hot water that Shabbos eve. However, in Da'at Kedoshim it is written that one who is accustomed to washing his head with hot water every Shabbos eve, can wash his head with hot water even on this Shabbos.