Use your "repair and deduct" remedy to get this heater fixed (linked below).
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Instead of using the repair and deduct remedy, a tenant can abandon (move out of) a defective rental unit. This remedy is called the" abandonment"remedy. A tenant might use the abandonment remedy where the defects would cost more than one month's rent to repair,but this is not a requirement of the remedy. The abandonment remedy has most of the same requirements and basic steps as the repair and deduct remedy.
In order to use the abandonment remedy, the rental unit must have substandard conditions that affect the tenant's health and safety, and that substantially breach the implied warranty of habitability. (I think lack of heat qualifies.) If the tenant uses this remedy properly, the tenant is not responsible for paying further rent once he or she has abandoned the rental unit.
The basic requirements and steps for lawfully abandoning a rental unit are:
1. The defects must be serious and directly related to the tenant's health and safety.
2. The tenant or the tenant's family, guests, or pets must not have caused the defects that require repair.
3. The tenant must inform the landlord, either orally or in writing, of the repairs that are needed.
4. The tenant must give the landlord a reasonable period of time to make the needed repairs.
5. If the landlord doesn't make the repairs within a reasonable period of time, the tenant should notify the landlord in writing of the tenant's reasons for moving and then actually move out. The tenant should return all the rental unit's keys to the landlord. The notice should be mailed or delivered .
Keep a copy of the written notice and any inspection reports and photographs or videos.