The phone itself it is too powerful for the size of the device and not that efficient (though it fares better than the previous SoCs in efficiency department), however the software is well optimized. The heat is quite evenly spread on the shell of the phone, where the top side below the camera is slightly warmer than the rest. To know how thoughful Sony was about this issue Z5 and Z5 premium have heat speaders with heatpipes!
The Qualcomm Snapdragon 810 (MSM8994) SoC has rougly the performance of an Atom x5-Z8500 CPU (take this affirmation with a grain of salt as it difers on some notable points) that is used on some small laptops. Those laptops are passivelly cooled by have a much larger area to dissipate the heat.
If I'm not mistaken, the 810 has a maximum TDP of 4W (although Sony could have limited this to 2~3W), that ends up in generated heat, and the SoC will throttle down to avoid going up in flames, however it can reach quite high temperatures and can be further throttled down by the mainboard sensors.
I have a Z5c, for me an operational temperature up to 55ºC is 'normal'. 65ºC is the hot maximum (reached when gaming) and if I notice it going past 70ºC I'll turn off the device or avoid using it for a bit.
IDK about the setup for Sony Z5/Z5c, but many manufacturers set the phone to throttle down when skin (outside shell) temperature reaches 45ºC, regardless of the SoC actual temperature. Most devices I know of never go past 50ºC to the touch (unless they are actually on fire).
With regard to throttling, the 810 SoC throttles down quite heavily just after 2 mins of heavy usage (however consider that it can do quite a lot on those 2 mins at those power levels). When updating the system for the first time it went past 70ºC for me and took 20mins or so, when doing it the second time (Marshmallow 6.0.1), I grabbed a wine cooling sleeve and put the phone in it (not kidding), even then it reached +40ºC on the SoC. I've also tested this with Antutu and it can go from 70k points in an hot day, to 98k points inside the wine cooling sleeve.
Taking all that in consideration, the phone gets warm to the touch with normal use, and slightly hot when playing somewhat demanding games (Galaxy on Fire, Pokemon Go, etc).
While this is not troublesome right away, the heat kills the battery and other components longevity. If you think your phone is getting too hot, consider what services your are running on the background and consider turning Stamina Mode on. If that doesn't help and you are not using it that heavily, then some wrong might be going on with your device (either software or hardware)...
The high power consumption from the SoC together with all the other components (screen, GPS, WiFi, etc) exacerbates the high temperatures as the energy has to go somewhere.
If you use the camera to record 4K for too long (definition of long can be broad) I know that the phone will overheat and stop the camera app.
