How to force users to logout after X minutes of inactivity using Rules, Views?
Drupalmodules.com shows two potential modules:

Session Expire - "Expires rows from the session table older than a certain time."

Automated Logout - "This module provides a site administrator the ability to log users out after a specified time of inactivity."

Either module would probably be able to give you the functionality you want. The automated logout module looks like it could give you a timer to show how much longer a user has before being logged out.