Why would there be a need for advise on Passwords. Simple they are really not intuitive at all. So here we have what I see as the most asked questions about Passwords in Thunderbird, and perhaps a little background on the passwords used.
How do I change my password.
The simple answer is you don't. You delete your password.
On the toolbar > Options > Security >Passwords there is a show saved password button. Clicking it shows all the saved passwords and offers the opportunity to delete them. If the password Thunderbird has is wrong this is what you must do. Next time you check your mail Thunderbird will ask you for your password. If you click the save option in the box asking for your password your new password will be saved.
Master Password does not protect my Mails.
This is 100% correct. The master Password is not designed as an application password. It's sole purpose is to protect your saved passwords with a password of their own. There is a really good article on Master Passwords on the MozillaZine web site.
The people who code Thunderbird are very unlikely to provide an application password. Why? Well the truth is that Thunderbird stores all of your mail in plain text files. Having an application password protecting your mail is fairly pointless when all of the mail is available to anyone who has a text editor and access to your computer. If you want to protect your mail and I mean seriously instead of with a dinky password such as is offered by the Profile password add-on, use the user accounts and passwords built into your operating system.