A space heater is not a substitute for building heat, and two kinds that people still buy are illegal to use in New York City. If the apartment is cold during heat season, the first call is the front desk, not a hardware store.

What the city prohibits
Kerosene heaters and propane space heaters are illegal in New York City. A gas stove or a charcoal grill is not a heater. Both of those warnings are on the city's heat and hot water page, in the section on staying safe in the cold, because they are how apartments fill with carbon monoxide.
The same page says the apartment needs a working smoke alarm and a working carbon monoxide detector. If a carbon monoxide alarm sounds, or you smell gas, open a window, leave, and call 911.
If you use an electric heater anyway
The Fire Department's winter guidance, as quoted by HPD, is specific. Plug the heater directly into a wall outlet, not an extension cord. Keep furniture, curtains, and anything else that can burn at least three feet away. Do not leave it running when you leave the room or go to sleep. Do not hang clothes on it to dry.
None of that makes an electric heater a right under the lease. The Anthem's published house rules do not list a space-heater policy. Ask the concierge before you bring one in. A heater that the city allows can still be something the lease restricts.
Why it is the wrong fix here
Heat is included in the rent at 222 East 34th Street. Electric is not. A plug-in heater moves the problem onto your Con Edison bill and does nothing about a boiler, a valve, or a unit that is not putting out heat. If the inside temperature is below the legal line — 68°F during the day when it is under 55°F outside, or 62°F overnight — that is a heat complaint, not a shopping errand.
Call the desk first. If it is not fixed, call 311. The rule and the safety notes are on HPD's heat page. Questions about a specific apartment are faster in person: schedule a tour or call (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