I do not think the pool at SSB is heated. Not to worry though... It's Jamaica mon... and the hot tub IS heated! We have been to SSB in December three years in a row and while the pool is sometimes refreshingly cool, it has never been close to a no-go.
Coincidentally to your question, an interesting water temperature contrast exists between the White River that flows into the sea at SSB and the sea water itself. One can sense "patches" of cool river water melding into the warmer sea water right off the beach. A situation that make SSB all the more unique and delightful to experience!