iPhone app that displays temperature as a notification badge
There are several Weather Apps that perform this function. The one I am currently using (as I live in Canada and it has good Canadian weather support) is Degrees.

You could also try Weather Live or eWeather HD. I'm sure there are many more.

One limitation of those badges, if you live in a part of the world like mine, is lack of negative numbers in the badge. Since I use Celsius, this is an issue even this time of year. :)