Hi:
Just entering here cause I have the same problem. (Yes, after upgrading to El Capitan, Mail fires up to 200% CPU for a few minutes, and repeats that each time I check for new emails.)
I tried all the suggestions here (including removing log files, rebuilding/reindexing/synchronizing, changing several settings in Preferences > Accounts, removing and recreating the accounts, completely uninstalling Avast, etc.), but things did not change. I even created a new user and recreated the accounts from scratch, to no avail.
The problem appears to be related to an IMAP account that has ~1500 mailboxes, since it goes away when I disable that account. I am not an IMAP expert, but from the log files it appears as if each time Mail checks the account it loops through and checks each of the 1500 mailboxes over and over again (I can provide parts of the log files if that is of any use). I would have expected that some "flag" would tell the program to check only those mailboxes that did change.
What about those here still experiencing the problem? Do you also have an IMAP account with lots of mailboxes?
Thanks,
Mariano