Overheating issues with Sony cameras are nothing new - they have been going on with some models since at least 2010 (with the Sony a33 and a55 cameras). There are now several new reports that the latest a6300 camera also overheats during video recording:
"Sadly pros can’t even rely on the A6300 as a B-camera due to the overheating, especially not for any kind of live filming or interview work at all." (eoshd)
"Unlike my a5100 where i could just turn the switch on/off and it would just keep on shooting with a6300 if i turn it off and on the message appears again that it overheated and the camera shuts down. waited no kidding 3-4 min and turn it back on... same isssue turned off in less then 1 min." (dpreview user forum)
"Got my a6300 as a "B" camera to my a7SII on March 11. I've used it exactly 4 times as a "B" camera while shooting the main footage with my a7SII workhorse. All 4 times, the a6300 went into overheat mode and shut down about 20 minutes into filming.... and that's not 20 minutes of continuous recording either, just being on." (dpreview)
In some cases, the a6300 displayed overheating warning, but continued to record videooverhea for 29 minutes: