Seems pretty clear someone is launching a pretty big brute force attack against the site., probably using known passwords from sources like the Adobe cache (although that's pure speculation..).
I've been getting these emails for days, and my poor account has been inactive for ages. Most of the IPs hitting me are located throughout EU and Asia, leading me to believe it's the work if a botnet.
Whatever the case, it has nothing to do with Heartbleed. If you know anything about the exploit, you'd know if they'd used it (which is NOT by any means easy), they would not be getting passwords wrong and would not be hitting accounts like mine that haven't been used in years.