The Med warms up all through the summer and only loses heat slowly after that. It's often as warm in December as the English Channel is in June. The coldest month is March, after a further three months of losing heat faster than the winter sun can put it back. In October I would expect the sea might be warmer than the pool in Turkey.
There is a nice little site called seatemperature.net which, as the name suggests, lets you enter a place name and see the current and year-round water temperatures.