What you need is Popper. Popper reads the new emails from POP3 and IMAP email servers and notifies about the number, subject, sender and time of new emails in the indicator applet and via a notification bubble.
How to install?
Press Ctrl+Alt+T to open the terminal and run the following command:
sudo apt-get install popper
How to configure?
Press the super key (windows key) and search for popper.
Open the Popper configurator and select "start popper automatically after login".
Now open the Thunderbird, and goto account settings through edit menu and select server settings under your Email Address and copy the server name and port number.
Go back to Popper configurator and select the "Account" tab
select "add" to add new email address, Fill the fields like this:
Name: Any name of your choice
Server: Paste the server address hare that you just copied from Thunderbird
User: Your real email address
Password: Password of your email address
Port: Paste the port number hare that you copied from Thunderbird and select 'SSL only'
Select IMAP if your email provider sports IMAP (Gmail, Yahoo and GMX)
Set the check frequency (how often should popper check for new mails).
Now open the "Test" tab of Popper configurator:
and hit "Test Email Connection", You should see a success message "OK Authentication Complete" if not than check your email address and other settings again.
Hit "Save and Exit". That's it.