In Thunderbird, when you receive new mail, an alert will pop up in the lower right corner of the screen (at least on Windows). Some people think it stays up for too long. Others feel that it goes away too fast. There is actually a setting for the duration of the new mail alert, that users can set.
In Thunderbird, go to Tools–>Options, open the Advanced section, select the General tab, then click on “Config Editor.” In the Config Editor, search for the preference alerts.totalOpenTime. Double-click on it, to change the value. Set the value to the amount of milliseconds you want the alert to stay up.