How to measure heat in a Manhattan apartment?
The first step would be to measure the room temperature yourself with a quality thermometer to be certain that the landlord is in violation. In daytime hours, the temperature is required to be at least 68, overnight (between 10pm - 6am), the temperature is allowed to drop to 55 degrees. But the rules don't kick in until the outside temperature drops below 55 and are only in force from Oct 1st - May 31st. The city provides a chart to summarize the rules:



Neither the City Housing Maintenance Code nor the Heat/Hot Water FAQ are  specific on the mechanics of the measurement:


  §  27-2029  Minimum temperature to be maintained. a. During the
  period   from October first through May thirty-first,
  centrally-supplied heat, in   any dwelling in which such heat is
  required to  be  provided,  shall  be   furnished  so  as to maintain,
  in every portion of such dwelling used or   occupied for living
  purposes:
  
  (1) between the hours of six a. m. and ten p. m., a temperature of  at   least  sixty-eight  degrees  Fahrenheit whenever the outside
  temperature   falls below fifty-five degrees; and
  
  (2) between the hours of ten p. m. and six a. m., a temperature of  at   least  fifty-five  degrees  Fahrenheit  whenever the outside
  temperature   falls below forty degrees.


However, since the code does state that every portion of such dwelling has to meet the minimum temperature, then I don't think that measuring temperature above a radiator would demonstrate compliance, as that only demonstrates that some heat is being delivered to the apartment, not that sufficient heat is delivered.

Plug-in heating devices are not included in their measurements - they do not measure the heat in a room warmed by such a device:


  Since the use of an auxiliary heating device,  e.g., space heater,
  will not provide an  accurate room temperature for the purpose  of
  issuing a violation, housing inspectors  will not measure the room
  temperature in a  room that is receiving heat from an auxiliary 
  heating device.


So don't feel that if you can use a plug-in heater to keep a room warm that you can't file a complaint if the central heat can't warm all rooms to the legally required minimums.

According to the Department of Housing Preservation and Development, if the Landlord does not fix the problem, the next step would be to file a complaint with the City:


  Tenants who are cold in their apartments should first attempt to
  notify the building owner, managing agent or superintendent. If heat
  is not restored, the tenant should call the City's Customer Service
  Center at 311 (311 can be accessed outside of New York City by dialing
  (212) NEW YORK). For the hearing impaired, the TTY number is (212)
  504-4115. The Center is open 24-hours a day, seven-days a week.  (You
  may also file a complaint at  311ONLINE for heat and hot water
  conditions.)


The city will then contact your landlord and/or you to verify that the problem as not been resolved and to schedule an inspection to verify non-compliance and issue a violation if appropriate.

For cases of continued non-compliance, the city may even hire a vendor to resolve the problem, and bill the landlord for the repairs.