I've also noticed some overheating on the bottom plate yesterday. That happened while trying to take a photo of a stationary subject with the 23mm, trying to get autofocus at its very minimum focusing distance and in very low light conditions. In a few of my attempts, I've been clearly trying to focus too close, beyond the specifications of the lens, even if just by a tiny margin, which caused the lens to hunt for focus several times. That resulted in the clearly slightly warm bottom plate and a hit in the battery charge left. The bottom plate was not that hot, but I could still clearly notice that it became warmer.
Like someone else suggested, this could well be similar to the issues experienced by many iPhone users after the installation of a software update on their mobiles, which resulted in overheating and poor battery life, most probably due to a memory leakage caused by the upgrade. I do hope, therefore, that this issue be fixed by Fuji with a firmware update.
As it stands, the battery on the X-Pro2 dies way too quickly than it could ever be accepted by even ordinary users.