Is it possible to keep favicon but clean other temporary internet files and cookies?
Nope, just visit the site again and it will come back.
You can keep a favicon if you open the Temporary Internet Files folder, find the icon and then copy it to another folder. Depending upon how a webpage is written the favicon may be in one of your systems temp folders like: C:\Windows\Temp
Note: Internet Explorer will give you a warning about copying any files from the Temporary Internet Files folder. After you've copied the favicon you can then right click the favorites shortcut and set it to the favicon you've stored elsewhere.
Damn I cant believe I missed that. I found this thread and saw a post by Tarun that said you cant keep them. Well a couple of posts underneath his post was yours with how to keep them. Sorry Pwong.
I forgot I even posted that in that other thread. That other thread has much better instructions as well.