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Weatherbug works. It has a persistent temperature in the notification bar and when your main screen is off it goes to the second screen.
I have looked at tons of weather radar apps and the one app I find to have the best radar is Weatherbug. Smooth, very detailed and accurate.
Not sure if I'm missing something? But I've been using the app for about a year and no complaints. The widgets are nice for my S5 and the weather is quite accurate.
I use Weather Bug: https://play.google.com/store/apps/details?id=com.aws.android
I used SparkBug in the WeatherBug app to show me the location of lightning strikes.