High cpu temps

I recently purchased an older Dell Studio 1535 laptop from Ebay, mostly just for me to learn how to work on these things.  This LT seems just fine as far as working order but has a failed display screen.  I'm using the machine with an external monitor and that works just fine, so there's nothing wrong with the video adapter IMO.  What I'm have a question about is internal cpu temps that are high.  I've installed Speedfan to monitor the temps and things are fairly good temp wise until I access the Internet through the wireless adapter.  Then the temps shoot up to close to 200 deg F.  I'm wondering what the problem could be........a bad wireless adapter??  I have another laptop pretty much exactly the same and it's temps stay nice and cool all the time.  I might mention that the first thing I did when I got this thing is to go in and remove the fan and heat sink to make sure it was super clean.  Could it also need  a new application of paste between the cpu and heat sink?