Wearing Shorts in Turkey

It's fine to wear shorts in most areas, but not if you are planning to visit a mosque. I would also probably avoid them if you were planning to visit a more conservative area. But definitely shorts are fine for just walking around, although if it were me, I would make sure the shorts are on the long-ish side—nothing too short.

I'll echo Mardee's comment that you will not be able to go in mosques wearing shorts (applies to men and women) or a skirt that falls above the knee. Your wife will also need to cover her hair and shoulders with a scarf to go in the mosque. If you are worried about heat, an option is convertible hiking pants that have the zip off lower legs. Istanbul is a little more flexible with dress code but if you're going to rural areas or Konya, shorts would not be seen as appropriate attire in any situation.

We visited Turkey during a heat wave and wore longish shorts the whole time except for inside mosques.

Our stops included Istanbul and Cappadocia, and then towns along the coast — Antalya, Kas, Patara, Dalyan, Datca and Marmaris.