After 10 years, I think it's time to clean the dust out
If you've never opened a mini before, it's really not as bad as it looks. Use a putty knife or a thin butter knife, be patient with it, and they're pretty easy to crack the shell off. After that it's a couple screws and cables to lift the drive assembly off which'll give you easy access to the heatsink and fan. If you're feeling adventurous, repasting it is a solid idea too. The heatsink is held on with a few snap clips that go through the logic board; just be careful undoing them so as not to break 'em and you'll be fine ^_^