I signed up here specifically to share my experience:
I cannot recommend the 16 incher with AMD iGPU after a total of 3 years of use, at least if you (like me some time ago) connect a 2560 * 1080 display (have gone through USB-C -> Displayport adapter/cable, USB-C -> HDMI adapter/cable and all possible constellations, the problem was always the same).
I even put a notebook cooler under the laptop to mitigate the problem.
It is suspected that there is a driver bug here (or a general software problem), since it does not occur with resolutions like 4K, at least for me (see below).
The dedicated graphics chip draws over 18W of power (which generates corresponding heat), and the fans spin at maximum speed (around 5400 rpm) after a short time
Then, after a while, the kernel task starts up to limit the temperature and reduce the load, and the device becomes unusable until you disconnect the monitor.
I have now once test a new 4K monitor and additionally a full HD monitor (1920 * 1080) connected (also with a USB-C -> HDMI adapter) and lo and behold:
The graphics card only draws 5-10 watts (in any case, no longer a constant 18W), which makes the fans run slower at about 3400 rpm (they are still audible, hence the docking station, see below).
Likewise, when only the Full HD monitor is connected, or when I lower the resolution of the other monitor from 2560 * 1080 to 1920 * 1080.
This was a pure chance find that more than surprised me and seems to confirm the thesis with the driver bug.
If it were really a pure overload, the problem should not decrease but on the contrary intensify when connecting a monitor with a higher resolution (and even a second one).
So the problem seems to exist only at certain resolutions (at least for me).
Of course, I can't speak for all constellations, but feel free to try it out yourself, maybe it will help one or the other.
For me, the whole thing was reproducible - but only after I figured it out.
Nobody expects that the thing runs more smoothly with a monitor with a higher resolution and a second monitor.
I have now opted (instead of a new 4K monitor) for a DisplayLink docking station (only the iGPU is used, as the docking station handles the rendering with its DisplayLink driver) to solve this problem.
When browsing, the fans even only run at 1600 (minimum) - 2000 rpm instead of 5400 rpm.
(Thanks a lot @ateslik and @connormac for posting the link to macrumors, where I read about this suggestion)
Now the MBP is really absolutely quiet and almost inaudible while surfing (a dream compared to before).
This is obviously nothing for graphics-intensive applications.
But I don't use those, and the silence/fan speed below 2000 rpm is more important to me than graphics power
Therefore, it became the docking station and not a new 4K monitor.
The whole thing is an absolute shame.
To put it bluntly, the 2013 MBP runs even quieter and, on balance, smoother (because no kernel task kicks in).
