You're right Mike. From outside, I simply can't figure out where the heat-sink is located. Should I open up my system for that?
Only you can make that determination, you just have to balance out your level of ability, with your willingness to a risk. Be careful, as not to supply any static electricity, to anything metal inside, unless you know it to be ground or you are otherwise grounded. (obviously I'm assuming you know what I mean, otherwise I'd recommend just Pushing as much air "threw" the case as possible. If you do decide to open it, this heat-sinks vary in appearance, but are often just a bent piece of copper tubing/rod that will be attached to a flat plate to make better contact with the CPU, etc. Just be sure to avoid separating the plate from the CPU, unless you really feel like diving in and have some type of thermal compound to replace the existing older dryer paste.
I have put my hands on old desktop CPUs before, but barely have a clue about laptops.
Just think
very tiny screws, and much tighter spaces, with little in the way of
extra space!
But I wanna solve it by myself anyway rather than taking it to any hardware store (my warranty has just expired, but I don't think that heat-sink falls under warranty!

). What do you suggest? Take a chance and open it up?
I know the feeling, again, I don't want to say "yes" then your next start with an "Oops!" It halfway between a cell phone and a desktop, I think you can judge from past experience.
I don't know if you read any of the links posted by Greg (post#7,) but they may help you figure out with more certainty what the problem actually is, as we are simply looking toward a possible cause, by using more of a statistical method. They should contain well-documented, easy-to-follow directions.
Obviously, it can't hurt to "properly" get the dust out of you laptop's ventilation system whether it's the cause or not, It would surely be eventually.
And while I don't have any links for you right now, It wouldn't hurt to have an application that reveals your system/HDD/CPU/etc.. temperatures. Of the top of my head you could use
Piriform's Speccy which will also let you see many other properties of your laptop, as well as save them to a file for later comparison or upload for us to get a better understanding of a problem you may seem to have.
Good luck!
Mike