End of August will be hot but I don't think there will be much difference in temperature between the Aegean and Med coasts, it may be a couple of degrees hotter in the Med though. It will likely be in the low to mid 30s, although it can get hotter than that on some days. Evenings will be very warm.
There are some nice resorts on the Bodrum Peninsual you could look at. Bitez is a lovely resort, not too busy but not so quiet. There is some good accomodation there, plenty of restaurants, a few bars and a nice beach. It is also just 5 minutes away by car from the lively resort of Gumbet so you could go there for a day of an evening out. It is also just 15 minutes away from Bodrum, so a great position.
There is a waterpark about 15 minutes away and you can do some good trips too, like a boat trip, jeep safari etc.
If you want to know any more about the are just let me know as I have been going there for years and I lived out there for a few years