Have you ever blown the dust out of it? It may be a simple solution to the problem.
I live in a high dust area, so I make a habit of blowing out my laptop monthly with low pressure air at work.
Of course, you may be right, and the fan is on its last legs, or already dead. Or it could be a dying battery or the hard drive heating up. Depends on where in the laptop the heat is coming from.
On HP laptops, when the fan goes, I usually find out when the graphics go bananas.