Notification of email to mobile phone

[PFJ]

Hi, every month my mobile service provider presents me with 300 free webtexts. I simply log on using Firefox from my bookmarks and firefox has my password so it just opens the correct page to begin entering my txt message..

Is there anyway I can use this facility to notify me that a message has arrived in my Thunderbird Inbox while my PC is online?

Regards
PFJ