When the number of transgressors increased, the Sages began to prohibit this. However, the large bathhouses [ambatyaot] in cities, one may stroll through them as usual and need not be concerned about the prohibitions of Shabbat, even if he sweats while doing so.
The bathhouses in the big cities consisted of several large rooms. It was customary to walk through them for purposes other than bathing. The heating in most of these bathhouses was under the floor, so simply walking through the bathhouse would cause one to sweat.
And the Gemara asks: What are these transgressors? The Gemara answers: Rabbi Shimon ben Pazi said that Rabbi Yehoshua ben Levi said in the name of bar Kappara: Initially, people would bathe even on Shabbat in hot water that was heated before Shabbat. The bathhouse attendants began to heat water on Shabbat and say that it was heated before Shabbat. Therefore, the Sages prohibited bathing in hot water and permitted sweating. And they would still bathe in hot water and say: We are sweating, and that is why we entered the bathhouse. Therefore, the Sages prohibited sweating and permitted bathing in the hot springs of Tiberias. And people would still bathe in hot water heated by fire and say: We bathed in the hot springs of Tiberias. Therefore, they prohibited even the hot springs of Tiberias and permitted them to bathe in cold water. When the Sages saw that their decrees were not upheld by the people because of their stringency, they permitted them to bathe in the hot springs of Tiberias, and the decree prohibiting sweating remained in place.
According to the Ran, the Gemara does not mean to say that the attendants actually heated the water on Shabbat by lighting a fire and boiling it. Indeed, the general principle is that Jews are never suspected of willfully desecrating the Shabbat. Rather, the statement must be understood to mean that the attendants added wood to the fire just before Shabbat and sealed the openings of the bathhouse. This act was prohibited lest the attendants come to stir the coals. This explanation is found in the Talmud Yerushalmi.