The landlord's failure to provide heat is a breach of your lease. Your remedy against your landlord for this failure depends on the lease terms. For a variety of reasons, it is difficult for commercial tenants to get reimbursed for losses due to the landlord's breach of the lease. Commercial leases usually prohibit tenants from deducting rent due to make up for losses due to landlord breaches of the lease or negligence. The tenant often has no option but to sue the landlord to recover for these types of losses. Since you appear interested in negotiating a renewal lease than leaving, suing the landlord my not be your best option right now.
You should meet with a lawyer to discuss this problem.
Dear Commercial New York tenant:
Maybe you want to engage an attorney to assist you in negotiating a renewal in an office space where you claim the landlord breached the lease, so that your new lease may contain some tenant beneficial terms that will address the concerns you discovered about the limited right you had in the current lease to enforce any basic simple promise of performance that the owner made and then did not carry out.
Yes you are right. Assuming that you provided notice to the landlord in the manner stated in the lease, then the landlord willfully chose to ignore you and your tenant and the obligations of landlord stated in the lease.
The landlord breached the lease and yet the lease likely had no process to force the landlord to provide heat and to maintain the radiators to have heat. And, in the real world, the landlord stuck it to you and your partner and got away with it.
Unless you have contemporaneously made records of the actual and daily affect on your business caused by the landlord forcing you and your partner to work in unheated offices, then you will likely not have a good chance of proving monetary damages. You could have sought an injunction in a breach of lease lawsuit in Supreme Court, but then you would not be discussing a renewal lease now.
So this may be the time to tinker with the lease writing process and if the landlord is not willing to concede that you have simple and expeditious remedies that you may invoke to compel performance in the future, then you may consider looking at another location with a landlord with a proven record of providing heat in the cold season.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
You should meet with an attorney to review your lease and advise you.
It is unlikely you can get damages for lost business because that is difficult to quantify. But you should be compensated for the time you could not inhabit the space because it was too cold.