Thanks for replying.
I actually bought the a6500 and have been happy about it so far.
But to answer my own questions, should others be wondering too. I haven´t had any problems at all with overheating.
The screen dims when shooting in 4K and 1080p 120fps, and it can really be hard to see anything in the display when shooting in bright sunlight around noon, but a thing I wasn´t aware of, coming from DSLR, is that the viewfinder shows everything the lcd does except the histogram, so that have helped me a lot. However it can be hard when using a stabilizer.
I have noticed the issues with rolling shutter as well. It´s worst in 4K. I could follow a person walking though.