Thanks for the quick response. I did not see that string in my /plugins/ folder, but when I searched the root I discovered this:
/home/content/##/#######/html/wp-admin/includes/file.php, line 928 $temp_file_name = $context . 'temp-write-test-' . time();
Does this mean that one of my plugins is calling a function that triggers this? By the way, the # symbols I had in my example for temp-write-test-####### was for the numerical value, which I can now see is a timestamp based on the time() function reference.