i dont know , i tried twice with the HP app , i have the deskjet 1050This might be an issue with your machine or interference with some of your programs, only, @yoka.
I have been using the HP Printer and HP Scanner full suite of programs and apps with a Surface, Surface Pro 2, Surface Pro 3, and Surface Book. No overheating problems on any of them.
Check the %CPU when the HP processes are running by using the Task Manager.