Can CPU intensive apps cause sudden shutdowns? Lately my Droid Incredible has been shutting down spontaneously when using my GPS for periods over 30 or 45 minutes.  After the shutdown the back of the phone is pretty hot (and that's with a case on it).  I kept my other services to a bare minimum when using the GPS.  

Could this be a battery overdraw (or overload with it connected to a charger)? If not, could some services (GPS, CPU-intensive games/apps, etc) or a combo of services cause the CPU to overheat and shutdown (much like a laptop when it gets too hot when the CPU is overworked with no additional cooling)?
Yes 

Overworking the CPU is what creates the intense heat, this intense heat is detected by the OS and shutdowns the phone to protect your hardware. (A PC works just the same).