They might be important, depending on whether they're in use, but chances are they are quite expendable. Those are files that programs briefly create to do some task. If you want to remove these to reclaim space on your hard drive, be cautious.
Chances are that old .TMP files can be harmlessly removed.
But I would not nuke any temporary files that are new, particularly if they were created on the same day you're doing the disk cleaning. There's a chance the file might still be in use by the application that created it. If you're still concerned, use an uninstall program that will compress and archive the files, rather than just deleting them. That way, if an application complains that it's missing a file, you can restore it. These are files that have been changed and there are now newer versions.