The Physics of Pool Temperature

To understand how much heat a pool needs, first you must understand how much heat it loses.

A pool loses heat at night or in inclement weather at a quantifiable rate, this rate is then used to determine the amount and type of heat needed to keep a pool at a given temperature.
Heat Losses
Swimming Pool heat loss occurs primarily at the surface where the evaporation of water accounts for this loss. This is the reason for the tremendous net effect of a pool cover.
Inground pools lose only about 10% of the total losses through the wall of the pool into the ground or through the lines removing and returning water to the pool in the normal course of daily filtration cycles.
Pool Covers reduce most if not all of the evaporative losses from the pool when in use. With this component of heat loss being 70% a cover with a small R value can achieve as much as a 75% reduction in heating costs when used.
Heat Gains
Swimming pools gain heat naturally during the day by absorbing the infrared radiation from the sun. An open pool gains almost twice the amount of the sun's energy than a screened pool due to the blocking effect of the screen enclosure, very similar to an umbrella with holes in it. The net result in the Central Florida area is a pool that is 6-8 Deg. F. warmer than it's screened counterpart.

Temperatures for Screened Unheated Swimming Pool
(Assumes Central Florida, Unshaded Pool with average 4.5 ft. depth)
Convert Celcius to Fahrenheit
Solar systems can be sized to gain anywhere from as little as 4 Deg. F up to as much as 16 Deg. F before cost effectiveness becomes an area of concern. The dilemma being that sizing for extreme conditions when the sun's energy is relatively weak and the outside ambient air temperatures are low means that the collector area required becomes cost prohibitive. On a 58 Deg. F. day swimming may not even be desirable, or said differently even if the pool is warm- is anyone in their bathing suit.