The laptop is a few weeks over 3 years old now. The blue screen problems started about a year ago, about 2 years after I bought the pc for grad school.
As to the temp I was giving 80c as the absolute highest I've seen it go since replacing the paste, it has been averaging in the 40s to 50s. It is an AMD. I am certainly endeavoring to keep the strain on the machine down, sadly the modern internet does not feel like playing along with so many video ads.
As for changing parts I don't have a clue how I could to that since it is a laptop and the noted lack of cash to throw at the problem. Of course is the problem only shows up while the pc is using more intense processes I am not sure how to diagnose a specific component since I would think you would need most of them running.