As I rebuilt my computer, I realized that the heat sink had been dislodged during travel and that the thermal paste had dried out and possibly even become dirty. The CPU was idle at about 60 degrees Celsius and it would reach almost 100 degrees within less than a minute of running Prime95. I ordered a small tube of Arctic Silver 5 Thermal Paste and as soon as it arrived, I cleaned and changed the thermal paste. The temperatures are now around 40 while idle and in the 60s while at full load. Finally, I can game without worrying about the CPU overheating. The process was easy and all I needed were Q-Tips and rubbing alcohol according to YouTube. Pictures of the process can be seen below.
The Lost Digit 