I am starting to think that I accidentally interrupted something during the first installation, or something like that. I created a new partition on my hard drive and did a fresh install of Zorin - this time with absolutely no problems at all. The fan hasn't gone into hyperdrive once, and it's been a couple of hours of use, installing my favorite programs, and the laptop has remained consistently cool to the touch.
Here's the screenshot of Psensor from just a little while ago:
Thanks so much to everyone for the suggestions. I installed both Stacer and Psensor recommended by StarTrekker, along with TLP as recommended by Aravisian. I'm looking forward to playing with Zorin without worrying that I'm going to fry my laptop. lol