If you want to be as close as possible to Oludeniz you should look around the Hisaronu/Ovacik area. Fethiye town is even further away (a 20-minute dolmus ride) from the beach at Olu.
I'm not sure if there's any maps of the area on this site, but to give you an idea, the first place you'll come to once arriving from the airport will be Fethiye town (it's a working town, but the harbour there is beautiful and well worth visiting), you'll then head up the mountain and after about 10 minutes you'll come to Ovacik (very quiet resort). Ovacik leads into Hisaronu (a 5-minute drive along) where it's much busier - and has lots of restaurants/bars running along its main roads. But there are quiet parts of Hisaronu too (places located away from the centre)
From Hisaronu it's a 10-minute drive down the opposite side of the mountain (from where you came up from Fethiye town) to Oludeniz beach.
Maverick is right: it is slightly cooler up in the mountain, but only marginally so. Fethiye town gets VERY hot - but I've never found Oludeniz particularly humid, or much hotter than Hisaronu.
Hope you find what you're looking for.
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Strawberry