Heat Sink kit or CPU Fan replacement...

I "inherited" my daughters' HP DV5215US notebook (we got her a new one for college) - I'm in the process of "tuning it up". I've just replaced her cracked hinges (new bezel, lid, hinges, etc.) and will probably replace the HDD (up it to a 7200rpm, 250GB) and throw more ram in it.

HOWEVER, I've noticed it runs REALLY HOT -- like burn your legs hot... The air coming out of the rear/bottom is very warm. (While I had it apart for the hinge replacement, etc., I cleaned everything I could see (and not see) to remove dust, etc.)

Since I feel 'some' air coming out, I don't know if it's the fan itself not working right or if it's the heat sink causing the problem. Is there a way to definitively diagnose this? If not, which would be the best one to replace first? (Both parts are about the same price ($45 USD) each.

Suggestions, comments...??

Thanks in advance (you folks have ALWAYS come through for me when I've had the rare need post!)

Maggie :confused

 

Mmmm ... also perhaps try it on a surface suck as a table ... I find with mine its ok on hard, flat surface, but If I put it on a bed or something It almost burns a hole through the sheets, also if it comes to it, you can buy cooling pads that have inbuilt fans, they push onto the laptop to keep it cool, best one I've seen has 3 inbuilt fans, 2 USB ports inbuilt and is powered via USB ...