That's just the worst-case scenario, but it's good to be prepared. The file system runs certain consistency checks which can result in the creation of many small TMP files, though they won't all be called the same thing nor be 0 bytes in size. It's possible these files are related to some sort of app activity.
CHKDSK /R should reveal whether there's reason to worry about the drive's health.
My Computer
Computer Manufacturer/Model Number
Multiple machines in various stages of decomposition.
You'll have to be a bit more descriptive than that. What was the result of attempting to run CHKDSK /R? Was the operation itself successful, and if so did it find any problems on the drive? In particular, was the "bad sector" count anything other than zero?
My Computer
Computer Manufacturer/Model Number
Multiple machines in various stages of decomposition.