If the laptop is heating up, that is very likely the problem. I would recommend you test it but since you can't boot that might be kinda hard... Ideally, I would leave the laptop on at the BIOS temperature monitor screen. Try that if you can manage to make it boot again.
If it is a heating problem you could try the following:
Open the laptop up and clean it thoroughly using compressed air. Make sure you clean the CPU fan, heatsink and air intake and exit grilles.
If the previous step makes no difference you may need to change the thermal paste between the CPU and its heatsink. You will need to remove the heatsink, carefully scrape off all the old thermal paste from both the CPU and the heatsink and then apply a new layer of paste. Bear in mind that once you remove the heatsink from the CPU, the old thermal paste is destroyed and you will have to apply a new layer. So don't try this unless you have some paste available.
I can't guarantee that this will help but it seems likely. If you do this and still have the same problem you will at least know that there is a hardware problem somewhere.