Do you have root access to the system? I'm not sure why you wouldn't be able to create the temp directory where the old one was (that is, if that was the default location). This might not be the problem anyways, but worth a shot.
Are you using different versions of PHP? Is the new box running a different linux distro than the old one? A lot of times different versions/distros use different paths for the same things.
Also, have Apache permissions been configured correctly?