Legal Question in Landlord & Tenant Law in New Jersey

You need to evict the tenant. Not repairing the heat means burst pipes. You have an ample basis to evict and not to repair the heat give the tenant a defense.

If you or your lawyer file an eviction suit, your tenant will have a habitability defense if the performance of the heater is so poor that the premises is deemed to be not habitable by the judge. You might lose the eviction suit but probably not more. Conversely, the tenant who is seriously behind in rent may default or may not be able to come up with the back rent that the court should require. If you were my client, I would advise you to file an eviction action based on the facts that you have told me in your question.

See also: http://info.corbettlaw.net/lawguru.htm