Probably, since such plugin will not exist, it will be necessary that you make as new plugin.
This is a technical (side) advice for users who know Linux, PHP and MySQL rather than the answer.
- Logged in time is saved in "loggedin" field in qa_users table.
- You'll have to check it on a regular basis in some way.
(e.g. Real CRON, virtual CRON like WordPress, etc)