You may set a cookie when login is successful:
Response.Cookies.Add(new HttpCookie("login_status", "1"));
And when user presses "Log out", you either delete the cookie or set it to another value:
Response.Cookies.Add(new HttpCookie("login_status", "0"));
Then it's easy to check in Page_Load event of the login page:
HttpCookie loginStatusCookie = Request.Cookies["login_status"];
if(loginStatusCookie != null && loginStatusCookie.Value == "1")
{
//User did not log out explicitly.
//Display timeout message.
}
else
{
//User either logged out or it is his/her first visit.
//Display usual greeting.
}