Yes. If you go into the detailed settings for the "Clear history when Firefox closes" feature, you can pick and choose different categories to clear.

Those settings are accessible here:

"3-bar" menu button (or Tools menu) > Options > Privacy

To reveal the controls, set the drop-down to "Firefox will: Use custom settings for history" (screen shot attached)

More info: Settings for privacy, browsing history and do-not-track

Note that Firefox won't use the disk cache if you use "Clear history when Firefox closes" to clear the cache (see the about:cache page). Only the memory cache is used in that case.

You can also do it manually thru an add-on.

Go to the Mozilla Add-ons Web Page {web link} (There’s a lot of good stuff here) and search for cache.

My thanks to everyone. Problem solved.