Overheating running Zorin on Dell Inspiron

I also had an overheating issue but it was on a Lenovo Yoga. It only seemed to happen when I was running VM's, as I like to run VirtualBox or VMWare with Windows on it. With the fan cranking and then the sudden shutdown I was sure I had a thermal issue. I picked up an app called "auto-cpufreq" and ran the "stats" to check on my core frequencies and temps and sure enough the laptop would go full-burn to 4.2Ghz and 99c until it shutdown. Installing the auto-cpufreq daemon allowed me to take control of the throttling. I've still got plenty of speed and no more shutdowns.
Hope this helps!