Upgrading the studio 15 (1535)

I currently have:

CPU: Intel Pentium Dual Core @ 2.0Ghz

RAM: 4GB DDR2

HDD: 300GB

GPU: Mobility Radeon 4630 (or something like that)

Basically I hate my processor, I chose it because it was the cheapest option and I know that I can upgrade it myself. Im going to purchase a Core 2 series CPU soon and what I would like to know is the following:

- Im aware that all core 2 processors that I can purchase have the same socket LGA775, purchasing one online, will it fit into this laptop? They have the same socket I know, but some processors of the same socket may be a little larger topwise.

-Say I bought a high end (3.0Ghz +) Duo or perhaps even a high/middle end Quad core (which is what id prefer) would the heat be an issue? I havent opened this baby up yet, so im not too sure if the cooling would be adequite? Thats my main concern, spend £120+ quid on a processor only to find the heat is too much for this laptop to handle and it shorts out.

So yes, anyone have experience in this matter? Also, im aware dell could upgrade it for me - but I dont need them to :]  Thanks in advance for any help you lovely people can provide :D

EDIT: Just to make sure, this is the processor I plan on getting: Intel Core 2 Quad 8400 2.66GHz LGA775