You want to use GMail's IMAP setting.
UPDATE: Assuming TB3
ImapMail – Mail Synch and Cache
Assuming you are using IMAP with your mail accounts, you will have an ImapMail folder, caching email and headers for your Imap accounts. If you take a look into this directory you’ll find sub-folders for each of your accounts. If you have “Message Synchronization” activated (which, I believe, is the default), you should have a local cache of all your mail in this folder.
If you’d prefer to disable this feature to regain disk space, you can do the following:
- Delete the contents of the ImapMail/mail.domain.tld/ folder (where mail.domain.tld is your mail server(s)).
- Disable “Message Synchronization” in Edit > Account Settings > Synchronization and Storage
- I would suggest leaving the remaining settings at their defaults. This post doesn’t cover them.
Resource: Disable Thunderbird 3 Bloat!