I regularly check the temperature in Bodrum and occasionaly on Kos if the weather station is not reporting in Bodrum. I have to say that it appears to be slightly cooler on average in Kos, e.g today the maximum temperature in Bodrum was 34c against 30c in Kos.
My wife and best friend went to our villa in BODRUM ( Gumusluk ) late October and spent every day on the beach in glorious sunshine , whilst 8 miles over the water in Kos it rained almost every day. I would imagine the temperatures in Bodrum town would be higher than Kos, it is normally several degrees higher than other parts of the peninsular mainly due to the lack of breeze due to all of the buildings.
Kos town - where the weather is measured is on the exposed tip of the island - so gets the wind from three directions including north and northwest, the same directions as Turgutreis, Gumuşluk,Yalikavak and Gundogan enjoy ... in summer.
Yes Bodrum faces the south and being an ancient harbour town too, is largely sheltered from both the winter storms from the north and the N/ NW winds in summer, and the natural harbour protects the boats from the SE winds.
Bodrum is the warmest spot on the peninsula- summer and winter, but it does get the breeze like anywhere on the west coast. If you want real stifling go south to the Marmaris to Alanya coastline....in summer.