A. The water of a bathhouse that got heated on its own on Shabbos:
A bathhouse which its fire is fueled from the outside, under [the bathhouse], if one closed before Shabbos those holes through which the [water in the] bathhouse heats up from, then it is permitted to bathe in its water immediately after Shabbos being that [the water] had not been heated at all on Shabbos.
However if its holes had not been plugged from before Shabbos then even though it heated up on its own on Shabbos [through one having stoked the fire right before Shabbos] nevertheless in the evening one must wait the amount of time it takes to heat it being that it was heated in a prohibited way. As it is forbidden for its holes to be left open on Shabbos when there is fire under it due to a decree that one may come to stoke the coals on Shabbos.
B. A bathhouse which was heated on Shabbos by a gentile:
Majority gentile population: A city with a Jewish and gentile population which has a bathhouse that is bathed in on Shabbos, if [the city] has a majority gentile population it is permitted to bathe in the water immediately after Shabbos being that one can assume that it was heated on Shabbos on behalf of gentiles which are the majority of the population.
Majority Jewish population: [However] if majority of the population are Jews then one must wait [after Shabbos] the amount of time it takes to heat [the water].
Half-Half: Furthermore] even if the population is [exactly] half [Jewish] and half [gentile] one must wait the above amount of time because it can be assumed that it was heated on Shabbos for both [Jew and gentile].
If one began heating the water before Shabbos and it did not reach its half way point by the commencement of Shabbos, it is forbidden for all Jews to benefit from it until enough time passes after Shabbos for the water to heat.
If a gentile heated it on Shabbos then if majority of the customers are Jews one must wait until enough time passes after Shabbos for it to be able to heat up.
If the water was heated by a Jew on Shabbos what is the law?
It is permitted to be used by all other Jews immediately after Shabbos.
If one visits a country club which heats their water on Shabbos may one bathe in that water after Shabbos?
If it was heated by a Jew then yes. If it was heated by a gentile then one may only enter the heated water if enough time passes after Shabbos for the pool to have been heated, if majority of its customers are Jewish.
 Seemingly this is referring to a case that the water was not heated to its half way point from before Shabbos. However even then Tzaruch Iyun from chapter 254 Q&A there.
 As although on Shabbos itself only gentiles bathe in it, nevertheless the main intention of heating it was so that the water be heated for the Jews to be able to use immediately after Shabbos. [Mishneh Berurah 37]
 See The laws of Cooking chapter 2 Halacha 1