The New Jersey instructions say that if you have applied for an ITIN and not received it yet, attach a copy of the W-7 to your NJ return.
Another option--if you are expecting a refund from NJ-- is to hold off filing the return until you get the ITIN back from the IRS. Penalties for late filing are based on what you owe, so if you are expecting a refund, there is no actual penalty for filing late.
The NY temporary number won't mean anything to NJ.
