Does heating swimming pool water from 27°C to 29°C cost as much energy as heating from 25°C to 27°C?

Answer

To raise the temperature of 1 kg of water by 1 Kelvin (or 1 degree Celsius) requires a constant amount of energy, which is given by the specific heat. For water it is 4186 Joule / kg / Kelvin. It does not matter whether you go from 20 to 21, or from 50 to 51 degrees Celsius. In practice, you may have to take into account heat loss at the surface of the pool. But in itself the required energy is the same.