i5 3570 with a cooler designed for 65w cpus?

[Torquel29]

I wanna start by saying i am really not that good with computer stuff.Recently i got rid of my fx 4100 and got a i5 3570 and a mobo.I am tight on money,the guy who sold me the mobo gave me a cpu fan "Deep Cool CK-11508" As a gift and i thought this could not be worse than a stock fan,i wont OC nice deal! After putting the system together i checked the cpu temp and it was around 40 at idle and 70 when gaming.This cpu is 77w but my 95 w fx 4100 with its death,dusty fan was much cooler than this.Then i checked the fan's website and there it said "Deep Cool CK-11508" was for 65 w cpu's.Learning this and seeing those temps made me thinking i should change this fan but i really dont have the money.So my question is will this be a problem? Can it be really worse than a stock cooler ? I used the paste under the fan when it came out of the box,can i lower the temps 7-10 degrees if i get a nice thermal paste from friend and go on like that?(Really tight on money) Sorry for my english and long post.

 

[mdd1963]

IS the fan on high speed? Is it variable, and can you set it to high/medium high without excessive noise? (I doubt anew application of paste will lower temps much, truthfully, but, won't hurt to try, and, you can save the new thermal paste for the next sink)

 

[Torquel29]

It is working at 2100 rpm most of the time,does not make any noise actual.The fans website says that its max rpm is 2200 so i dont think i can rise its speed any more.
Edit: The reason i asked about doing new thermal paste is that there was paste under the fan,and i put some more on the cpu before putting them together.The paste i put on cpu was a baaaddddd brand,so a bad thermal paste.Maybe too much bad paste from the diffrent brands made things worse?