How can I turn off the notifications?

Climate supports notifications as of the v1.2 update. However, there aren’t any fine grained controls to suppress specific notifications from occuring. (These are planned for v1.3)

You can completely turn off notifications for Climate via the global Notifications Systems Preference pane. As you can see, you can also configure how the notifications are displayed, as well as if you want sounds to also be played.

Notifications Systems Preference pane