The window dims because of a compiz setting , which dims the windows of programs which are not responding.
You can change the setting, if you have
Open it and go to Fading Window plugin. There is a settings named Dim unresponsive windows. Uncheck the setting if you don't want the dimming. But I don't recommend it, since it tells you which program is not responding.
Why Not responding?
The application may seem to be not responding while starting up sometimes. Mostly it happens when it does some background activities, such as fetching settings, loading files and trying to connect to the Internet etc.
I think, the most likely cause in your case is, You get large number of new messages in your email account everyday and thunderbird was trying to fetch those emails. But It is not a big problem since it quickly becomes responsive after the operation. It may also related with your Internet connection speed, which may be slowing down fetching and syncing information with your email account.