What exactly gets "worn out" and damaged by heat?
There are really two different types of temperature stress, cyclying and sustained heat.  

Just about any part is susceptible to failure from large number of temperature cycles.  Each different type of material in a part expands and contracts at different rates.  Of course packages are designed to accomodate this, and materials are chosen or specifically formulated for common thermal expansion responses, but stresses occur nonetheless.  Eventually those stresses being applied back and forth enough times will break something.

Sustained heat is different.  Silicon stops being a semiconductor, and silicon transistors therefore stop working, at around 150&deg;C. Heating a IC to that temperature won't directly hurt it, other than it won't work as intended.  However, that "not working as intended" could include excessive currents, which then cause more heat.  Eventually something melts and the part is irreversibly damaged.  Some chips, like modern processors, have such high density that failing to get rid of the heat for even a few seconds from the die can cause something to melt.  Consider the size of a high end processor die compared to the end of a soldering iron, and then consider that there can be 10s of Watts dumped into the die, and that the soldering iron gets to solder-melting temperatures at that same power level.  Getting rid of heat is a major issue with such chips.  That is why they come with integrated heat sinks and fans nowadays.  Take off the heat sink and fan, and your processor is toast in short order.  Or, it shuts itself down to protect itself.  Either way, your PC isn't going to run.

Electrolytic capacitors are different from most other electronic components in that they inherently go bad over time.  Heat accelerates this.  Running a electrolytic cap at 100&deg;C, even without cycling, will degrade it much more rapidly than at 50&deg;C.