From MozillaZine Knowledge Base
ISYS , X1 professional client and Nuance Paperport are commercial products that have built-in support for Thunderbird. Exalead used to have a free version of Exalead one:desktop with built-in support for Thunderbird but now only the commercial version is available. The free and commercial versions of Gavri Search explicitly support Thunderbird.
Due to the similarity between Eudora, Netscape, Mozilla Suite, SeaMonkey, and Thunderbird mailbox formats and profiles, most desktop search applications that support Thunderbird support those other applications too.
Spotlight support for Thunderbird was added in version 3, though you had to set mail.spotlight.enable true to enable the user interface.  . Thunderbird supports integration with Windows Search (Vista and later versions) if you enable Tools -> Options -> Advanced -> General -> System Integration -> Allow Windows Search to search messages.