At first I wanted to create a complex structure to display the data, but after a few data sketches it was clear that it was way too complicated. Too complicated for someone just trying to view the weather.
As a result, I ended up just simplifying the whole thing and showing the data as simple and clearly as I could. Throwing in a splash of colour to represent the current weather condition, based on the colour guide suggestion provided.
The main screen real estate shows the current temperature, and icon representing the current weather, the location, wind speed, chance of precipitation and humidity levels. While the bottom shows the temperature for the next days, that you can scroll through independently.
I originally had all the fields in the bottom section as well, but when looking back on it, the fields were way too crowded. So I just left the day and temperature.
The location screen again is trying to keep it simple, with the search bar right at the top to search for locations right away. Then with your saved locations below, you can edit them to remove or change the order, etc. And finally placing the Temp˚ logo at the bottom of this window to make sure the branding is still seen without conflicting with the users experience.
Here's a mockup of a different colour scheme based on the current weather.