Not that I remember. Still, no need to go for an old model, phones with the current 845 come at really affordable prices.
835 is fine. though I had to turn off some of the programs running behind the screen, like xiaomi ai and that
I think you should be looking for phone type overheat issues instead. Not all phones treat cpu as deserved...
As mentioned, it was the 810 series. Qualcomm usually designs their own architecture that is backwards compatible with ARM. They were not able to make their architecture updates in time so for the 810 series they went with slightly modified base ARM architecture. The problem was that the job was rushed, and as a result the 810 series had overheating issues. They did release some patches way later to help mitigate some of the overheating issues though. So yes, 810 is the only one which had serious overheating issues due to it being different than all other snapdragons.