There is no exact season for spa cure in general, but there are some seasons preferable for different diseases.
Summer is more suitable for the diseases like rheumatism, neuralgia, and diabetes while Spring and Autumn are more suitable for diseases of stomach, intestine, liver and nerve cases.
May and September can be prefered for a twice-a-year cure.
However, in some regions of Turkey, any season can be prefered since they have a warm climate.