Iv'e done this walk on my first Turkish visit. I presume you mean from the Ghost Town at Kayakoy to Olu Deniz? I actually walked from Ovacik to Hisaronu to the Ghost town then over the hills to Olu. I walked this on the first week in August when the temparature was pushing toward the mid forties. I was fortuanate that it was the day before i finished my holiday so i was very brown and moreover had some resillience to the sun.
My advice would be to take plenty of water (3 litres) as the walk took me more than 6 hours, bearing in mind i got lost at one point. The path from the Ghost Town to Olu takes you up and over rugged out crops initially before you decend into a pine forest, and if you miss the turn left in the path as i did, will take you down to the shoreline. I then had to walk back to the top! The route has red or blue arrows painted on the rocks that you follow, just make sure you dont miss any!
I was on my own, and bearing in mind i didn,t see a soul until i got to Olu, had some concern over twisting my ankle or something and having no one to come to my aid. As i said it was hot so make sure you are covered up and have suitable sun block. Also tell someone where you are going, my wife was getting frantic back at the hotel.
I say all this because i concider that i was inadequately dressed, had half a litre of water, and when you think i had only intended to walk to the Ghost Town, bit off more than i could chew (got a taxi from Olu back to the hotel), but would definately do it again as the views are more than rewarding.