delete permission the temp file stays

When I deny users the ability to delete files within a shared folder it creates a problem; when a file is opened a temp file is generated which normally closes down when the original file is closed however under the deny delete permission the temp file stays and is not removed, I end up with thousands of temp files, how can this be resolved I can’t believe this is normal. At the end of the day all I want to do is give the everyone group denying rights to delete anything and only specify certainusers full access. Can you please help. Thanks in advance.