edit: make sure the bios in the new computer can handle (see) all 80gigs of your drive. You can do this by updating to the most current bios firmware.
moving the HD shouldn't be a problem as long as you don't damage the drive while moving it. Since its a slave drive and you're not going to install a os on top of the data, no problems should occur cus the dtaa will be untouched. However, if you have installed progs on that drive, you'll need to re-install them.
I never had to put paste between my cpu & cooling fan. I'd say if you were instructed to do so by maunal or manufacturer, do it, otherwise i think you should be fine.
specs?