there are a few mekoros for a heter of taking a HOT shower. if you look in shmiras shabbas khilchata you will “essentially” find one.
also, if you look in shulchan shlomo you’ll find what your looking for from RSZ Aurbauch zt”l.
people, dont be so quick to say bnei torah dont shower b.c you are insulting RSZA…..