If you want to see the cached items, I would recommend turning on the Site manager -> Settings -> System -> Debug -> All -> Debug everything everywhere option.
Now, if you go to the Live site, to the page where you control is located, if you scroll to the bottom, there will be all debug information. You will be interested in the Caching section (usually is the second, right after the SQL section), where you can find an item Partial cache (YourWebpartID).