Many have had issues with overheating on both of the internal 4K models (a7S II and a7R II), but while those may not be fixable via firmware update, another simple issue is: the dreaded black sunspot, which can occur when shooting with the sun in the background, or when shooting with extremely bright/blown out specular highlights in the frame. It's worth noting that a number of cameras have had this issue, so the a7S II certainly isn't alone.

In the newest 1.1 firmware, Sony has fixed this problem:

This utility updates the ILCE-7SM2 camera firmware to version 1.10 to address a condition where a black spot may occur in a high intensity lighting part of a shooting scene.
Note: This condition is especially seen in PAL 25p, it rarely happens in NTSC 30p or 60p.

If you've just been shooting with the camera in the western hemisphere, it's possible you haven't run into this nearly as much, if at all, as those across the pond who shoot PAL natively. As proof of this fix, Wolfcrow posted this video that shows all different picture profiles shooting directly into the sun:

If you're in the US, you can head on over here to get the newest update, and if you're elsewhere in the world, be sure to visit the exact Sony site in your territory. 

Source: Sony