In order to deduct any portion of your rent due to defective heat, you must actually pay to have the heating system repaired and then you deduct the costs of such from the next month's rent after you have given notice to you landlord of the problem.From what you have written, it does not appear that you may legally deduct next month's rent due to lack of heat. However, I would speak with the landlord and the property management company as to a rental rebate due you for lack of adequate heat and the inconvenience caused.