A fan failure would fit with the symptoms.
Step one is get a canned air (I see them in pound shops here for a basic one) and give it a good squirt when it is running. Such things are a temporary fix most of the time though, and that is if it is dust that is causing it. The bearings in fans can often fail (or at least the grease in them turns into some kind of putty/gum) which means replacement thereof (maybe a bearing flush and regrease if you are lucky and know what you are doing), oh and of course said fan is likely custom to that model.
After that you are left with cleaning it properly. Difficulty varies massively between models -- I had a HP consumer thing the other month and it saw me have to pull it down into pieces (other than the screen and RAM everything came off, every screw, every ribbon) and was a nightmare. A business class HP of slightly older vintage a month later saw me pop the keyboard off and sort it, a mid tier consumer dell of a few years earlier still was a plate on the back cover and 4 screws to gain full access.