In Hoboken, the temp must be 65 degrees between 11 pm and 6 am... and 70 degrees the rest of the time.
If it's not, you can get the health department involved (201-420-2375) They can send a warning letter to your landlord, and if he does not fix it within a few days, they can issue a summons to fine him.
Below is a link with a wealth of info about landlord and tenant rights in NJ:
http://www.lsnjlaw.org/english/placeilive/rent/tenantsrights...