What to o if I’ve refused to pay rent because I was without heat for a month and have now been served an eviction notice?

You can try to raise a violation of the implied warranty of habitability (the obligation of the landlord to provide rental premises fit for their intended purpose--in this case, residence) due to the lack of hot water as a defense to eviction; the landlord's breach of this warranty can give tenants the right to withhold rent. If the landlord takes  you to court to get the eviction, make sure you show up for court with all the money--i.e. all the back rent-in a mony order. Explain to the judge that you are ready, willing, and able to pay and have only been withholding the rent because the landlord has refused to correct the problem.

Note, however, that if the landlord has been making efforts to fix it--they have sent someone 6 times, according to what you write--you may lose. The landlord is not expected to provide a perfect or defect-free rental unit, only to take reasonable steps to correct problems when they come up. While an argument could certainly be made that after this many tries, the landlord needs to take some more drastic action, like replacing the water heater entirely, a judge could conclude that the landlord has been doing what he should be doing--sending people to make repairs when you tell him about the problem--and has fulfilled his obligation. If the judge sees it that way, you may be evicted.

You therefore may wish to see about paying the rent to avoid eviction, if you would have nowhere to go if you lose--while you do have what appears to be (based on what you write) a viable defense, you cannot count on winning.