Probably because it cools down much faster there, due to higher relative surface (per mass). You can also see this simply by the difference in color.

My first guess would be less surface for contact, thus less heat transfer. But the corners are also colored differently, I'm not sure why that's the case. They probably cool down quicker?

I assumed the color difference is just that they are actually cooler, so yeah, they cool down quicker. And not just "quicker": the difference must be huge in order for it to be completely safe to grab the corners and actually dangerous to grab the faces. But why?