Most computer administrators would prefer to have early warnings of overheating, rather than be alerted by a pile of melted slag. Modern CPUs are capable of generating very high temperatures, and although they are designed to slow down or even shutdown when they get too hot, it doesn't take long for them to fail when they overheat severely, sometimes damaging other components as well. Server-quality hardware often has temperature monitoring and automatic shutdown features built-in, but frugal admins who rely on PC hardware must take some extra steps.
Most low-end PC motherboards these days include an onboard watchdog chip. An easy way to find out whether you have one is boot into your system BIOS. A hardware health page should display statistics. Most watchdog chips are LM78, I2C or "compatible" chips. Just having the chipset isn't enough because you also need software to capture and report the data. Linux users can install lm-sensors to keep an eye on CPU and case temperatures. lm-sensors monitor a large number of hardware health items, depending on what your watchdog chip supports: fan speeds, voltages, motherboard temperature and even chassis intrusion detection.
lm-sensors requires a few simple steps to get up and running on your system: Install the lm-sensors package; run the sensors-detect script and say Yes to everything; modprobe the drivers reported by sensors-detect; finally, either run the command-line sensors application to view your system statistics or use a graphical front-end like ksensors, sensors-applet or gkrellm.
The graphical sensors have simple checkboxes for configuring what type of alerts you want, such as e-mail or beeps. If they seem to be reporting incorrect values, go into /etc/sensors.conf to make adjustments. The file is well-commented and should tell you everything you need to know. If that's not enough, visit http://www.lm-sensors.org/ for more information. A comprehensive Sensors FAQ should also be included with your lm-sensors installation.