My SP3 has the fan running nowadays quite regularly. Been happening since the upgrade to W10. It warms up too but not too much. I have also noticed that battery life is quite a bit less with W10 as compared to W8.1. Maybe the two things are connected.
Edit: And display driver crashing quite frequently!!! Oh...I don't have the HP App you are referring to.
I do not have any HP printers any more. Got rid of them a long while a go. I now use Epson Printers. So, no HP printers, no HP app and no, I do not have a clue what you are talking about. It might work for you but it certainly is not going to work for me. Perhaps it might help if you were a bit more specific when you post.