From Mozilla Developer News:
If you already have Thunderbird 2.0.0.x, you will receive an automated update notification within 24 to 48 hours. This update can also be applied manually by selecting “Check for Updates…” from the Help menu starting later today.
For a list of changes and more information, please review the Thunderbird 126.96.36.199 Release Notes.
The security vulnerabilities addressed in Thunderbird 188.8.131.52 do not affect Thunderbird 1.5.0.x users, therefore, there is no update required for Thunderbird 1.5.0.x series users.