@eneuro
If any heat was getting soaked into the die, a shutter event would include this during subtraction of the flat field. If you look at miguelvp's photo of the hot ring, you see the outside ring is warmer than the data in the center. This shows that the lens isnt aligned properly, but most importantly, that the bottom flat(what the lens sits on) of inside the lens housing is reflecting the sensors heat back at itself. Also, I bet a good deal of money on the image circle is barely large enough to cover the sensor. Its made to a low cost, so its clearance will be tight.
A few people are tied up on this being a convection problem. A metal housing will heat fairly evenly, but it's not even directly sitting on a good heat conductor, so it isn't really able to get PCB heat. And its too far away from the sensor so there's a gap where glue takes up the space. This isn't a convection problem, it's a radiation problem. The shutter isn't responsible for this either. It covers the sensor entirely during a calibration. That's all it needs to do. Then it moves completely out of the way. I tested this as well as mike.
Look at the photo of the lens housing inside, and then look at the photo miguelvp made. Taken into consideration the problem gets worse with time (heat buildup), and you have your culprit. The sensor isn't visible to itself until it's warm enough that it radiates significant heat back off the lens housing onto itself. This throws the flatness off because it is adding to the data where it shouldnt be there at all. Use the high-low mode and look at ice, the hi is almost 20 degrees from low. Look at a hot object, the hi and low are close together. The radiation will always add to the scene, but the biggest difference will be on cold scenes. Hot scenes only have a minor impact. Scenes with wide temperature ranges won't show the gradient because the gradient only shows itself when the palette is squished to fill a small range.
The lens housing is too compact and as a result sits close to the sensor die. The die is small, so the focal point is closer to the lens, look at any phone camera. The smaller the die and lens ratio, the closer they must be together to achieve focus. This is one of the issues of a 12um sensor of this resolution. Its a compromise.