If you're new to databases then there are quite a few concepts to get your head around before diving into this. There are many ways you can achieve what you're trying to do. I made a diagram to show you how I would build the database for your system:
http://img191.imageshack.us/img191/3235/exampleg.jpg
Each department belongs to a site. You can see that the > indicates that a site can have many departments, and the | indicates that a department can only belong to one site.
The user table stores the information for users who log into the website.
When one of your users subscribes to a department, they can specify the frequency of their emails on the website. Their subscription would be stored in the subscription table. You can see that a user can have many subscriptions (as indicated by the >) but a subscription can only belong to one user.
Each subscription links to a department. Again, one subscription can only be for one department, but a department can be subscribed to many times by many users.
That's about all there is to it on the database end of things. To manage the frequency of subscriptions you would need a script to run every XX minutes/hours that looks at all the records in the subscription table and depending on their "frequency" will send out a temperature reading for the department that the subscription is linked to. The "frequency" value might be simple words like "daily", "weekly", or you might have codes like 01, 02, ...
I hope somewhere in all that babbling you find some useful information!

Please let me know if you need me to expand on or explain anything.