Depends where you are in Turkey, but the weather definitely gets cooler towards October and by November could be pretty bad - if you are in the far east, for example, then you would have rain, snow, freezing temperatures.
I would ensure that the house that you rent has a water heater as some places rely totally on solar to heat the water which makes for a very cold shower! over 6 years ago
Assuming you'd prefer to stay on a coastal region;
In september any place on agean or mediterranean coast will be fine to spend a month, the weather will be mild or even hot in some places. But this is the month when rainy days start. So get ready for shower for somedays.
In October the weather for the mentioned places are mild, and mostly wont bother you.
In November you have only the mediterranean coast as a choice. about 6 years ago