In extended use the camera seems to get hot
We are of course also aware of this, and are continuously working to improve, however; the large Medium Format sensor contained within the X1D demands the use of high-speed electronics and RAM to cope with the data transfer requirements for 30fps live-view and video.
Data transfer from the sensor and its associated system in conjunction with the EVF or rear display will generate heat in normal operation.
The body is built from aluminum and incorporates passive cooling. The heat is transferred from the processors and sensor thru the aluminum body; using this as a heat sink.
If the live view or video capture functions are used for extended periods of time the camera body will get warm. This is totally normal and is not a malfunction of the system.