Step #1) Since the Thermal Compound is the least expensive solution I would try another brand of silicon that has good reviews and apply it like I mentioned previously ( 1 small bead in the center with 4 small beads in a square about half way to each edge of the CPU.
If you can clean / remove the old paste using material (I use small white coffee filters) that does not leave any fibers behind (on the surface o the CPU). Apply a small amount of 90% Isopropyl Alcohol to the coffee filter and wipe the CPU clean (you may need to repeat the cleaning process until there is no evidence of the old compound on the filter).
Now let the CPU sit for about 20 minutes and then apply the paste / compound as shown below.
Now run Core Temp and see if the problem is resolved and post back how much cooler the CPU is under load.
- Hold off on buying the new fan until you try using the new paste as applied in step #1 to see if it solves the over heating problem.