This was applied to the Xperia Z5, but there was no confirmation of whether it was the same situation for the Xperia Z5 Compact. Unfortunately according to recent reports out of China (via Tech Grapple), it turns out that maybe the Xperia Z5 Compact was not given the same treatment because now there are users who are reporting that their Xperia Z5 Compact phones are overheating.
The overheating issues have gotten to the point where not only does the phone get hot (obviously), but it starts to get sluggish when users try to interact with the screen, making the touch laggy. In some cases, it would seem that the screen will not even respond to touch, and only after locking/unlocking it will it begin with work again.
Rebooting the phone seems to offer some kind of temporary fix as it allows the phone to cool, but ultimately it is not a permanent fix. No word on how widespread this issue is, but if you have an Xperia Z5 Compact that overheats, do let us know in the comments below.