'Battery Alert' appears before the 'press 'ESC' key for Start-up menu.', however, ' Cooling Fan Alert' appears after 'press 'ESC' key for Start-up menu.'

In my country, I don't know if I can find another brand  of silicon that has good reviews or not. What about applying the same silicon compound I have again with the way you have mentioned? 

If that is all you have then use it.

Also, I don't know what is Isopropyl Alcohol (rubbing alcohol) and white coffee filters, although I googled Isopropyl alcohol, and how much do they cost?  

Then use some type of cleaning fluid and cloth that does not leave any lint or oily film on the CPU.

I removed the old thermal compound with applying small amount of the new silicon compound, and then I wiped it.

Not a good means of removing the old thermal paste, remove the old thermal paste first and then apply the new paste.

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.

2. 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.

Thanks a lot,

In my country, I don't know if I can find another brand  of silicon that has good reviews or not.

What about applying the same silicon compound I have again with the way you have mentioned? 

Also, I don't know what is Isopropyl Alcohol and white coffee filters, although I googled Isopropyl alcohol, and how much do they cost?  I removed the old thermal compound with applying small amount of the new silicon compound, and then I wiped it.

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.

2. 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.

1st) See if you can find the brand of thermal paste you purchased and read the reviews: http://www.newegg.com/Thermal-Compound-Grease/SubCategory/ID-85

2nd) You need to replace the fan which is the important things on your list which is why I made the comment about eBay.

3rd) I have no answer as to why the strange readings.

Thanks a lot,

1st) no my thermal compound paste is not like what you have linked from newegg.com. That one you have linked its link is silver compound grease, however, mine is silicon. I have not found silver compound grease in my country. Yemen.

2nd) you meant that I must replace old fan with the new one fan which is sold for $50. It would be definitely solve the problem? Or the problem is not with old fan which was cleaned and it was like the new one. However, it is with thermal  compound I used.

1st) See if you can find the brand of thermal paste you purchased and read the reviews: http://www.newegg.com/Thermal-Compound-Grease/SubCategory/ID-85

2nd) You need to replace the fan which is the important things on your list which is why I made the comment about eBay.

3rd) I have no answer as to why the strange readings.