I am using Godaddy IMAP email with Thunderbird as my desktop client on Windows 7. The email service has unlimited mailbox size but the local Thunderbird is having troubles due to the large size of the inbox/outbox. I would like to take out old emails from IMAP server and backup them locally. After backing up the old email I would like to delete old email (older than let's say, 2012) from the server. Also I'd like to have them accessible from the local backup if ever needed in the future. This way I might be able to make Thunderbird fast and problem free.

Problem is, I am not able to find any instruction to do this in an automated way based on dates etc. I can find some links for Archiving, Compacting and Backup. But unable to find any tutorial about how to backup and archive it locally and delete the original emails from the server.