I think your choice of late September is more sensible than late August, especially if you have problems adjusting to the intensity of the sunshine. Late August would be great for water sports and sun tanning but not if you have plans to go out exploring the area.
September isn't bad in Turkey, though it depends where you plan to go. From experience,
weather is still very hot in the first few weeks of September tough the nights are cool, which is great as you'll be able to sleep easier.