Heat season in New York City runs from October 1 through May 31. During those months the owner has to keep the apartment warm under a specific rule, and hot water is required all year, not only in winter.

The temperature rule
Between 6:00am and 10:00pm, if the outside temperature is below 55°F, the inside temperature must be at least 68°F. Between 10:00pm and 6:00am, the inside temperature must be at least 62°F no matter what it is outside. Those figures come from the city's Housing Preservation and Development heat page, which is the page inspectors use.
An older city summary still describes the overnight rule as applying only when it is below 40°F outside. That is not what the current HPD page says. If you are checking whether the apartment is legally warm at night, use the 62°F rule.
Hot water is not seasonal
Hot water has to be provided 365 days a year at a constant minimum of 120°F. A cold shower in July is the same kind of complaint as a cold apartment in January. It is not something you wait until October to report.
What to do if the apartment is cold
Contact the building first. That is the step HPD tells tenants to take, because most outages are fixed faster by the people who run the boiler than by an inspector. If heat or hot water is not restored, file a complaint with 311 or at portal.311.nyc.gov. You can file anonymously. HPD may call the owner, try to reach you, and send an inspector.
An inspector can issue a heat violation during the day only if the outside temperature is below 55°F and the inside temperature is below 68°F. Overnight, the test is whether the inside temperature is below 62°F. If you are not home, the inspector leaves a card and may check another apartment.
What this building already includes
At The Anthem, heat, hot water, and cooking gas are included in the rent. Electric is not. A cold apartment is a building issue, not a bill you are supposed to solve with a plug-in heater. If the apartment is below the legal temperature after you have called the desk, 311 is the next step, not a space heater left running overnight.
This is a summary of the public rule, not legal advice. The current text is on HPD's heat and hot water page. To see a residence before heat season starts, browse available apartments or schedule a tour at (212) 684-3222.
Interested in Living at The Anthem?
Browse available studios, 1-, 2-, and 3-bedroom residences at 222 East 34th Street, Murray Hill — with video tours and 3D walkthroughs for every unit.
View Available Apartments Schedule a Tour