I bet it's harder to formulate a question that's less broad than writing the entire script from scratch. There's no "general format for accessing a weather web service". Nor to store that information in an object.

First, you need to define for yourself what kind of information you want to display. Current temperature is your data, but do you just want to display a number? (In that case, no graphic is needed). A graph with the temperature of the past X days? Something else? Furthermore, where is your data coming from? An HTML document? Some other web service (since you mention SOAP::Lite)? I know weather.com has HTML documents with weather information. I would use LWP::Simple, or lynx to retrieve the information. As for the object, well, if all you care about is a temperature, I wouldn't bother with an object. A scalar will do fine.

This script will be installed on a web server that I don't have permission to install new modules on

Reaaaaaaaaaaaaaaaaaaaaaaaaaaaally? And you can install a program? How does whatever method you use to install a program know whether what you are installing is a program and not a module? What about a file that can be used both as a program and a module? If you install that, does the web server disappear in a time-space singularity?

Abigail