Your external drive doesn't need any sort of drivers, so if it doesn't appear on the desktop immediately there are a couple of things we can do to get it going:
1. Open Disk Utility (found in Applications > Utilities) and select the external drive. Click on "First Aid" and then click "Repair Disk".
2. If that doesn't do it or you get errors, click on the "Erase" pane and click Erase. Note: this will reformat the drive, erasing all data. Don't do this if you have anything on the drive you need to save.
3. Attach the FW drive to any other macintosh - if another machine reads the drive and your new 'book doesn't, let us know and we'll troubleshoot from there.
Regarding heat - yes, these new macbooks are hot mothers, so you have to consider heat management whenever you use it. Don't place the book on a cloth surface, like a tablecloth, bedspread, or pillow. You'll suffocate the vents and heat up the book. Try to keep it out of direct sunlight especially. Consider one of those aluminum lap desks, those guys are wonders for heat management. Oddly enough, your actual lap is a pretty bad place to use a macbook, as your thighs have probably already complained. Your own body heat adds to the heat of the book, and then add in the crappy heat dissipation capability of the jeans/skirt/leather gimp outfit that you're wearing at the time.
Ask more questions if you need to, PM me for a quicker response!