I do have the issue during the hot days of the summer (35C New York City) and when I'm using the X1D on a tripod.Anyone with an X1D had overheating issues and/or unexpected shut downs?
The camera will shut down and reboot on its own.
The ARCA-SWISS plate that I'm using has some rubber to protect the camera body. This rubber is blocking the heat coming from body. As mentioned by others, the heat is dissipated by using the aluminum casing and in particular at the bottom of the camera.
So hot days, tripod plus long time on live view is definitely not a good mix for the X1D.
In my opinion, this is a design flaw and Hasselblad should work on it on the X2D. One solution could be to create some recessed lines at the bottom of the body to improve the surface of contact and especially when a tripod plate is mounted.