Frederick,
Thanks for the response.
This host is running PHP in safe mode with GID restrictions in effect. Thus, the PHP file requesting access and the file being written have to be owned by the same group.
All the wp-admin files have the correct group to write (or overwrite) files to those three directories.
However, it seems as though the function load() in w3-total-cache/lib/W3/Config.php tries to recreate the compiled config file for every page load where an administrator is logged in. It will also attempt to rewrite this file for every visitor if the check for the compiled config fails, regardless of what script is running.
Since not all scripts have the correct GIDs/permissions to write files under this safe mode restriction, there are lots of attempts to rewrite this file.
This is compounded by the fact that tempnam() doesn't work properly in safe mode either, so instead of it failing gracefully, the temporary files pile up.
I'll submit a support request via the plugin if you've got something that you'd like me to test.