Theme Egg

This is Weather Forecast widget plugin, You can add widget by installing this plugin. 
After Installing this plugin go to Appearence>>Widget and add widget to your sidebar.

Weather Forecast

This is Weather Forecast widget plugin, You can add widget by installing this plugin.

Tony Samperi

wp-ng-weather is a simple widget for WordPress, which allows you to put a weather widget in your website, by using a simple shortcode like this:
<blockquote>
[ng-weather api-key=”my-api-key” city=”Bergamo” locale=”it”]
</blockquote>
No coding is required! 
wp-ng-weather is a wrapper for Tony Samperi’s ng-weather (tonysamperi.github.io/ng-weather/), which is an AngularJS Directive. 
Weather data is got from http://www.openweathermap.org, but they need to track api usage. 
So you’ll need your personal API KEY to use this widget, see “Installation” to learn how to get one! 
With a FREE API KEY it’s possibile to make 60 calls per minute.
<h3>parameters</h3>
<ul>
<li>api-key: Your API KEY you got from openweathermap.org. REQUIRED</li>
<li>city: A string with the name of your city. This isn’t required if you set “city-id”</li>
<li>city-id: A string with the ID of your city. This isn’t required if you set “city”</li>
<li>locale: A string with your locale. “en” or “it” are supported at the moment. Default value “en”.</li>
</ul>

WP NG Weather

wp-ng-weather let's you put a weather widget anywhere in your blog

Weather Forecast vs WP NG Weather