How to clean the dust from my laptop?

I've never heard that opening a computer doesn't void warranty. If you damage something while in there, then that won't be covered but if you're just dusting there's no reason why you should damage anything unless you have zero common sense. I literally just finished removing caked on grime from the fan in my pc and its doing awesome now, nothing is out of the ordinary.

There really is no good way to clean out a laptop fan without taking it apart. The problem is that there's undoubtedly a massive wad of dust and hair and stuff between it and the heat sink. There's really no safe way to get this out without opening it up. Some people recommend to use compressed air to blow into the heat sink where the fan blows out, but all this does is jams up the fan and makes it run slow (or sometimes fail to run at all), thus compromising the cooling system. Since you have a warranty, I'd recommend getting a professional to fix it. That way, should they void your warranty, you can sue them for messing up your computer.