shuts down after a few minutes of heavy use

This for sure sounds like an overheating issue. What I would recommend doing is by cleaning your fans as they might be clogged with dust, which can make it much harder for them to keep the laptop from overheating.

You could also replace the thermal paste, but that would be quite difficult considering that you would need to get to the processor chip in order to do that, which would most likely involve removing the heat sink which tends to be quite difficult, so I would recommending finding a tutorial for doing that online for your laptop (make sure you know your laptop's model as different laptops require different procedures).