Ah, the old shorts and high heels question! Once upon a time it was a question that wasn't even asked. Yes, Daisy Duke was on the TV every single week in shorts and heels, but nobody outside of a club, or maybe a car show, dressed like that in real life. Then suddenly it was ok, and even I can do it.
For me personally, if I'm going to wear shorts, I'm going to wear sandals. Though I've modeled them before, I would never wear an enclosed shoe with shorts, unless I'm playing tennis. If I'm actually working outside, I'm covered head to toe (for sun protection), so it's not about the heat, it's about the style. I do usually wear open toe mules with shorts, and they do tend to have a wooden heel. But not always. I don't often wear stilettos with shorts, and I'm not 100% sure why. Perhaps stilettos with shorts still have that "clubby" look about them that I don't necessarily want to wear out and about under normal circumstances. Wedges also seem to work very well with shorts. For some reason, wedges seem to take the edge off the look.
Oddly enough, I do not have all that many pictures of me in shorts, probably because I've been doing this church outfit of the week things for some time, and I still will not wear shorts to church. Even though many people do this nowadays, it just seems wrong to me. Especially when I'm on the livestream camera that gets saved forever and ever. So I'll find some quick examples. I don't do long shorts, because they simply do not look good on me. I don't have a lot of real estate to waste covering it up.