Thunderbird now allows for web pages to be opened within the program and i think CC Cleaner and other address this.
Please try your post again, as it is not possible to assertain what you are asked, commenting on
As of version 3.19.x ccleaner has seperated thunderbird and firefox entries.
I have version 1.09.313 for Mac. At the time I posted this i couldn't see a way to add Thunderbird under the "Applications" section of the cleaner but now i see that it's included. Somebody was paying attention.
Moved to ccleaner for mac