I was in
Marmaris for New Year (travelled home on 6th Jan) a couple of years ago and the weather was like a nice spring here.
You won't need a thick coat - a leather jacket was enough for me and a couple of mornings it was nice and warm enough to have coffee sitting outside on the marina in the sun.
Be warned though, when it rains it rains (roads like rivers - well they were in
Icmeler anyway which is probably why the kerbs are so high there!!) so take a brolly!
I keep away from Marmaris in the summer, but enjoyed it in January - there's plenty open and going on as it's not just a holiday resort like Icmeler is.
Have a fab time!
Mazz