I have the Packard Bell OneTwo L5710 and it worked okay for a year before it started encountering problem with overheating and automatically shutting down. It was still under warranty, so I took it back and the supplier repaired it (but wouldn't tell me what was repaired). A year since that, it has started happening again. Usually when the CPU is loaded >50%I will notice that the fan suddenly stops working, and the CPU temps climb to 110-120 Celcius and then it just does a hard shutdown.
I would replace the fan, and apply new thermal paste after cleaning the old paste off; but if you don't have any paste, try the fan first. Newegg carries alot of sizes; your board may not have the holes necessary for a standard heatsink, so you may have to replace the fan only. You may also check for an extra connector off the power supply, and plug the fan directly into that, but then the noise may be high, so select the fan according to the rpm rating. 1500-2500 is adequate for cooling.
I have an L5831, which I think is very similar to L5710, and overheating (though no to the point of shut-down) has been a problem for a while. Like your own problem, it has been getting hotter over time.
I assumed this was because of a build up of fluff and dust so I opened the p.c. up yesterday to blow it out.
There was virtually no dust in there, because virtually no dust, or air can get in. There is a metal casing over all the works, which seems to be there mostly so you can wall mount the machine. The intake perforations in this case are tiny and few, and the top ventillation is not much better.
I put the machine together again, without replacing the internal metal cover and I now have a cool quiet machine, albiet one that might actually need dusting next time around.
Its gone form being the worst ventillated p.c. I have ever seen to being the best ventilated.