Looking for the db_cachedir in the settings.php file was the hint I needed. Thanks, sXi.
I didn't just want to comment out the line without understanding the consequences. After a little more research, here's the solution that worked for me:
By way of background, the one-click installation of WebCalendar prompts users for the location of the tmp directory. By default, the value is "/tmp." Not knowing any better, and seeing no obvious helpful hints in the wizard or the documentation, I left the default value as it was. Unfortunately, the wizard does not create such a directory, and no such directory existed under my web site's root (www.example.org).
To fix the problem, I:
1) used WebFTP to locate the settings.php file (it was under www.example.org/webcalendar/includes, which also was not intuitively obvious to me);
2) opened the settings.php file using the source editor;
3) found the line that sets db_cachedir (not difficult--it settings.php was a very short file);
4) simply removed the virgule ("/") so that the line now reads "db_cachedir: tmp" (without the quotation marks); and
5) saved the file.
Then I created a subdirectory named "tmp" in the webcalendar directory (i.e., www.example.org/webcalendar/tmp) and relaunched the program.
Problem solved. I suppose I could have just created a "tmp" subdirectory in the root, but then I wouldn't have all of my webcalendar files together.