When I see such a machine I'll tear it down, pull the heat sink, wipe off the heat sink compound and build it back up cleaning as I go. A fan check is down last.
I take it that you are going to be a laptop repair expert soon.
My computer sometimes locks up after using for awhile. I use a fan stand to help reduce temp. I replaced the internal cooling fan. I am still not sure it is working. Should I be able to hear the fan cycle on and off? Having replaced the fan, is there a temp sensor that may be defective? Any other suggestions will be helpful. I am far from a computer expert!