Bathing for a mourner during the seven days in cold water

Is a mourner allowed to bathe in cold water?

A mourner is prohibited from washing their entire body even in cold water, except for their face, hands, and feet, which may be washed in cold or lukewarm water that does not feel warm at all, but not in hot water. In places with great heat and excessive sweating, according to our teacher the rabbi, it is permitted to wash the body in cold water, and if necessary, one may be lenient even with soap and hot water.

Shulchan Aruch, Yoreh De'ah, Siman 381, Paragraph 1: "What is bathing? It is forbidden to wash the entire body, even in cold water; but the face, hands, and feet in hot water are forbidden; in cold water, it is permitted. If he is dirty with mud and excrement, he washes as usual and does not worry."

Therefore, in places with excessive sweating and if he washes for the cleanliness of his body and not for pleasure, it is similar to someone who is dirty with mud and excrement, about whom the Shulchan Aruch writes that he washes as usual and does not worry. It is also similar to an instenis in Siman 380, Paragraph 3. As written in the Jerusalem Talmud, Tractate Berachot, Chapter 2, Halacha 7: "This is said about bathing for pleasure, but bathing that is not for pleasure is permitted," as written in Mishnah Berurah, Siman 513, Sk 2.

In Pitchei Teshuva, Yoreh De'ah, Siman 381, Sk 1, it is brought in the name of Tiferet Le-Moshe, who wrote that even in lukewarm water it is forbidden if it is heated by the fire due to 'lo plug', and also it is not customary to bathe in overly hot water, and when bathing in hot water is forbidden, lukewarm water is forbidden. And the poskim wrote that even Tiferet Le-Moshe only forbade in lukewarm water where warmth is felt, but lukewarm water where cold is not felt and there is no warmth is permitted.