For not being relied on executing a huge e-mail-program (MS Outlook for instance) in background continuously or acessing an empty e-mail-box with a wrong expectation unnecessarily, you simply could use the tool MailCue. Hereupon you will be informed as there are new e-mails in your mailbox.

Other features:

You quickly can configurate the most important features by right-clicking on the e-mail-symbol in your tray-bar. Furthermore, the status-popup with the observated e-mail-accounts will open by a simple leftclick. It can be blanked out either by doing a click at the X or a right-click at the tray-symbol then. Additionally, remember to deactivate the popup-function as you stay in full-screen-mode. Otherwise it will be demolished as soon as a new e-mail comes in.

Note: For operating the software properly the taskbar must be positioned at the bottom of your desktop.