I had the same problem. After migrating from my old late 2006 MBP running Lion, to a brand new late 2013 rMBP running Mavericks, the Mail 7.1 Application constantly utilized one processor to a full extent, making a joke of the declared 9 hour battery life (reducing it to 3 or so).
I have spent several evenings investigating with no luck.
Only after I have made a grand pruning of old items, the problem went away. I cannot pinpoint the sole responsible, as all actions were executed in one batch (I suspect either the spelling library or internet plugins - as the Mail App kept running threads called "web content").
List of actions done (replace xxx with username), Mail and Safari must be stopped:
Removed inactive and unreachable email account (deactivated the account).
Deleted Envelope files from:
/Users/xxx/Library/Mail/V2/MailData/
(se other threads for instructions)
Removed old 3rd party spelling library from:
/Library/Spelling/
/Users/xxx/Library/Spelling/
Removed unused, old or unwanted Safari plug-ins:
/Library/Internet Plug-Ins/
/Users/xxx/Library/Internet Plug-Ins/
- AdobePDFViewer.plugin
- AdobePDFViewerNPAPI.plugin
- Flip4Mac WMV Plugin.plugin
- iPhotoPhotocast.plugin
- SharePointBrowserPlugin.plugin
- SharePointWebKitPlugin.webplugin
- Unity Web Player.plugin
Removed unused or unwanted startup items from:
/Users/xxx/Library/LaunchAgents/
/Library/LaunchAgents/
/Library/LaunchDaemons/
- com.adobe.AAM.Updater-1.0.plist
- com.adobe.ARM.df0ab5bbe6f698196fcc21e3c1e66dcb758bd911f4d637272d9d8109.plist
- com.adobe.fpsaud.plist
- com.adobe.SwitchBoard.plist
- com.bombich.ccc.plist
- com.google.keystone.agent.plist
- com.google.keystone.daemon.plist
- it.infn.lnf.network.AFSBackgrounder.plist
- org.ocsng.agent.plist
Viola, after a full restart and rebuild of Envelope files, Mail App is docile keeping its paws off my CPU when nothing is asked of it.