will a laptop cooling fan work with this laptop?

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http://www.bestbuy.com/site/Gateway+-+Laptop+with+Intel%26%23174%3B+Celeron%26%23174%3B+Processor+-+NightSky+Black/9574757.p?id=1218127626587&skuId=9574757

I am getting a new laptop, and this is what i can afford.. I have heard that this laptop overheats and starts to shut off a lot, something about a piece melting on the fan, if I get a cooling stand with it, the one that i plan to get is

http://www.bestbuy.com/site/Targus+-+Laptop+Chill+Mat+-+Black/Gray/9427042.p?skuId=9427042&id=1218103734860#tabbed-customerreviews

Do you think that it is going to stop that laptop from overheating? and one last question :X does every laptop fit into that cooling fan? dont answer this one if you cant im worried if that fan will atleast work haha