Well, this looks like an issue which can be prevented through software then.
Of course, that is the minimum, because without a software that prevent from it, you will alway have a bad feeling when measuring with DC level.
Perhaps we need a kind of egg timer that measure the DC over 400mV time and switch on a screensaver.

Oh...and it is time dependend, so I guess the main reason is heat. I have a aircon in my workshop, so never above 25degree. It is probably bader if you living and measuring in a country with 35 degree room temperature.
I am still waiting for the answer from Batroniks, perhaps they have to discuss a little with R&S

, so I can not open my RTB now, but I become curious how it looks inside, perhaps there is a way to optimize the cooling of the LMH.
TI wrote me they need a day to investigate it....
Olaf