This is much easier than I had imagined. At first I thought I need to do some programming with the SharePoint Object Model APIs. It turned out to be nothing of the sort.
Let us assume that you have a photograph located in your picture library named "pictures" at this URL:
The thumbnail for the above picture is located at:
As you can see, here's what I did:
1) tag a directory "_t" to the the URL just before the filename.
2) tag "_jpg" to the filename just before the extention. This would have been "_gif" if you are dealing with a GIF file.
Voila, if you point your browser to this tweaked URL you will get your thumbnail.
You will get a larger image if you use _w instead of _t.
Painless eh. . .