Thunderbird-Tray

Thunderbird-Tray is a handy and reliable application that minimizes Mozilla Thunderbird to the system tray and notifies you whenever you receive a new email.

Create a profile and assign a global keyboard shortcut

The configuration panel is the place you need to access in order to set the path to Thunderbird and enable the use of the executable name to detect the Thunderbird window, but you can also set the profile name.
In addition, you can choose the preferred language, enable the program to hide the tray icon when Thunderbird is shown, add "Write Mail" and "Open Address Book" to icon menu, as well as assign a global hotkey for the software. The latter feature greatly enhances ease of use.

New mail message pop-up and other parameters to tweak

Furthermore, you can configure events - launch and hide Thunderbird when the tray application starts (optionally give a start delay time), close Thunderbird when the tray exists, close the tray when Thunderbird exits or run the tray at system startup, and more.
When you receive an email, Thunderbird-Tray pops up a message. Simply click its title to automatically access it in the Thunderbird interface.

Performance and conclusion

The program uses a very low amount of system resources and it is easy to use by both beginners and experts. However, we tested it by sending several messages to an email account used in Thunderbird. The tool was unable to notify us of incoming emails in most cases. So, we had to double-click the tray icon to enter Thunderbird and finally receive that email notification.
All in all, Thunderbird-Tray certainly presents itself as a solution for receiving messages via Mozilla Thunderbird, but it needs some debugging.