Firstly it depends where you are. Near the coast or in the hills. Very quickly in parts of Puglia you are at over 1,000ft which has a fairly dramatic effect on night time temps. It then depends on how hardy you and your family are. We have friends that swim in their pool up here in Martina Franca from the middle of April but personally I wouldn't go near a pool till it is 24C . May is a funny month weather wise 2011 was gorgeous whilst last year was warm but cloudy, still normally towards the end of the month it has got itself sorted out.
Given the price of gas, oil and electricity are double that of the UK I would probably want to know more about the "heated" pool or the surcharge must be huge. Years ago we looked at about €100 a degree.
Remember in Cyprus querying where the pool heating equipment was and the owner pointing to the sun in the sky.