Sony has updated the firmware for Sony A6300 to version 1.10. Officially the changes are:
Improves overall stability and operability of the camera
Improves stability in picture shooting mode by optimizing temperature control (effects vary according to temperature).
so there is no direct mention to the overheating issue that affects this wonderful camera when shooting video (and, more rarely, when shooting stills), though there is a vague point to overall operability and surely some improvement has been done on overheating when shooting stills.
Already many people have tested the issue with video: some users report major improvements (much longer time before the camera shuts off for overheat), others report just a 10-15% of longer video shooting time.
Anyway, good news and we wait for some clarification from Sony for video or a new firmware upgrade .
The upgrade is available at this link (you need a good lever of battery charge to allow update).