Air: May to August about 15-30°C, September to April: 0-15°C. Water: May to August fine (a shorty will do), from September to April you need a wetsuit, in December/January it can get cold (around 0°C). January to August unpredictable, can be anything. September to December usually cloudy/rainy weather though in this period, especially when there's wind.
Petten beach is not a spot for beginners, there are strong currents and beach breakers. Lifeguards will check if you can kitesurf or not. If you are a beginner you are not allowed to surf this spot.