Apple Mail consuming lots of CPU

Since I've upgraded my MacBook Pro from Snow Leopard (10.6.8) to Mountain Lion Apple Mail has been behaving strangely – Activity Monitor shows Mail consuming about 100% CPU for hours at a time. Mail is often very sluggish at displaying messages. I've rebuilt my mailboxes (Mailbox > Rebuild) but that doesn't seem to help.

Is anybody else experiencing this? Any ideas about how to troubleshoot/fix it?