Besides whateve the city inspector is doing to help you, you have the following two options:1) Withhold rent until the heat is fixed--landlords have an obligation to provide rentals that are fit for habitation (for people to live in), and a lack of heat violates that obligation. If  and when the landord tries to evict you for nonpayment of rent, you raise the lack of habitability as a defense: the court can decline to evict for nonpayment and order the landlord to make repairs. IMPORTANT: a) make sure you have provided written demand to the landlord to fix the heat; b) keep the rent money separate and safe--you will likely have to deposit it in court in order to get your habitabiity defense heard. At the end of the matter, after the landlord fixes the heat, the court will release most, possibly all, of the withheld rent to the landlord, but may give a portion of it back to you for having put up with lack of heat for a time.2) If the heat is not repaired within a reasonable time--typically a few weeks, since these things can take time (e.g to get qualified repair people in, get any necessary parts, etc.) following written notice to the landlord of the failure to provide heat, the continued habitability violation may provide grounds for you terminate the lease early and move out without penalty for being "constructively"--or effectively--evicted by the lack of heat.