When you make a browser using the .NET control, you're not actually making a browser. You're basically just changing the look and feel of IE, adding or changing basic features, and often times, leaving out many features.

Since the WebBrowser control is basically a stripped down version of Internet Explorer, any temp files, cache, and/or history is stored in the same place as IE's folders.

So, using
System.Environment.SpecialFolder.InternetCache()

should allow you to get the path of the Cache for IE, which in turn will get the cache for your "browser."

From there, you can delete it programmatically.

This is all assuming you have not created your own location for your temp files.