I've tried using this widget on this site, in the right-hand sidebar:
WordPress is up to date, ie. 3.5.1 as of the date of this post.
I'm posting in the example short code (from your site) just to get it working before I customise location and image, etc. Unfortunately I can't seem to get past this error:
Warning: file_get_contents() [function.file-get-contents]: http:// wrapper is disabled in the server configuration by allow_url_fopen=0 in /nfs/c03/h04/mnt/52684/domains/binalongbay.com.au/html/wp-content/plugins/awesome-weather/awesome-weather.php on line 81
Is this something you've seen before, or can help with?