Assuming the fireplace is not the main source of heat (and this doesn't make the place inhabitable), it is really a contractual issue--i.e. What exactly does your lease provide for:
- who is responsible for repairs?
- does the tenant have to give written notice of a defect, giving the landlord 30 days (or some other number of days) to remedy the defect?
- is written notice required by the tenant prior to making repairs?
As people mentioned above, this most likely come down to what notices were sent to who and any responses (actual documentation). If there are any issues--e.g., you were responsible for the repair and failed to make it within a required time period after you received the required notice--then I would just pay the tenant and be done with it.
Assuming you fulfilled all your obligations under the lease (and it is the tenant at fault), and you decide to go to court, here are my 2 cents. If you hire a lawyer for this, you will not end up ahead (unless you get an attorney to do it for free). Were you planning on making the repair? If so, the practical answer (forget the legal answer on whether or not you win in court), get the repair paper work from the tenant and compare that to what you would have paid. Assuming the tenant's contractor performed the work satisfactorily, offer to pay the tenant whatever you would have ended up paying anyway (and the tenant can eat any additional cost he paid). I think this is the most reasonable approach.