Check the weather app settings. There should be a check box for displaying a notification. That would mean in the notification bar.
You may have more than one weather app operating, even if in the background. So, check your apps list in Settings>Applications>Manage Applications. If you see other weather apps, go into your app drawer, open each weather app and make sure the "notification" box is unchecked.
I have Beautiful Weather Home widget and also WeatherBug. Both have the option to have the temperature (or more) in the notification bar. I keep one operational so I can see the temp on other home pages beside the one with the weather app. Just saying'...