Do i have the right to insist on receiving the full rent because the central air unit needed to be repaired or replaced in may in new york

Your tenant is absolutely not entitled to a rent reduction for the inconvenience of two "unusually hot" spring days. The law does not require a landlord to provide air conditioning at all- only heat. Even if you agreed to provide air conditioning as part of the rental agreement, you were arguably under no obligation to do so that early in the season. However, you also say you've had other issues over the past five years with heat and plumbing.  If the issues were so serious as to force the tenant to vacate the apartment for significant amounts of time, that could amount to partial constructive eviction, warranting a rent reduction, in the event the tenant took you to court. But if the heat and plumbing issues were simply normal repairs and maintenance and, as you say, you made the repairs as quickly as possible, your tenant is not entitled to any rent reduction whatsoever. You sound like a responsible landlord- perhaps you should look for a more appreciative tenant at the end of this tenant's lease term.  And if there is no lease, you are only required to provide 30 days notice for the tenant to leave, and if the tenant does not do so after the 30 day period, you are free to evict the tenant.