First of all, if you don't have a lease then your are considered to be a month-to-month tenant.  Consequently, there is a legal landlord-tenant relationship and you have all of the rights of any other tenant. Specifically, youhave the right to the "warranty of habitability".  This is the right to live in a clean and safe premises.  Additionally, if you have to move out due to this situation, you have been "constructively evicted".  Accordingly, you can:Repair and deduct - You can fix the problem and charge the landlord for reimbursement;Withhold Rent - You can withhold any further rental payments until the heat is restored; orTerminate your lease - You can choose to end your tenancy and move.  You can also hold your landlord liable for reimbursement of any expenses incurred as a result of any move.  However, you need to consult with a landlord-tenant attorney before pursuing any of these self-help measures.  If you fail to follow the proper procedures for attempting any of the above remedies you could be held liable financially.  At this point either hire an lawyer or contact a tenants rights organization, Legal Aid, or the state/county bar association.  A  local law school clinic might also be of help to you.