Livre d'Or

One reason computers overheat is a fan failing. IIRC I've encountered this a couple of times. In desktop computers it's usually practical to diagnose and fix this as it's easy to look inside while the system is running and notice a still fan, and replacement components are readily available. Fitting them can involve a bit of swearing.

Another reason is that the thermal grease used to ensure good heat transfer between the CPU and heatsink degrades with time (or occasionally is badly installed in the first place). I have had this happen multiple times and it's probably what's going on in this graph. Diagnosing this can be a bit harder, but if you're sure that temperature is the problem this is IMHO the most likely cause. In desktop computers, it is practical to fix: replacement grease is readily available. Removing and replacing the heatsink may involve swearing.

Computers get dusty inside, and I assume that can impede airflow, though I've never yet had dust cause an overtemperature shutdown myself.

The bad news of course is that laptops are a lot fiddlier to work with than most desktop computers, raising the difficulty both of diagnosis and fix (and presumably raising the cost if you take it somewhere to be repaired).

There's not much you can do in software other than measure the temperature at various points in the system. Various applications support this and sometimes the BIOS setup screen will report system temperature(s) too.