I did that with 2009 thinkpad and it got much worse. I guess the cheap paste I used was worse than the 6 year old paste lenovo had used :( What _did_ help was

I did that with 2009 thinkpad and it got much worse. I guess the cheap paste I used was worse than the 6 year old paste lenovo had used :( What _did_ help was to take out the fan, clean it and then oil it carefully (too much oil or doing so without cleaning it first will only make things worse). You can also buy replacement fans, although original fans are quite expensive.