Tenancy Services had received 1271 calls seeking advice about insulation. Another 68 emails had been received regarding potential breaches of the law.
Mohammed Rafique, a taxi driver from Māngere, said the insulation in his three-bedroom house was not upgraded by the July 1 deadline. He was concerned because his son who lived with him occasionally had allergies which could be worsened by cold and damp environments.
When his two children stayed at his house, he ran two heaters at all hours.
Rafique said he was hesitant to make a complaint to the Tenancy Tribunal because it was difficult to find affordable rental properties and he was concerned his landlord could retaliate.
But after he raised it with his landlord, Karan Prasad, the insulation at his $480-a-week rental was upgraded on July 17.
Prasad, who co-owned several properties, said he managed to get the other properties insulated last year but was not able to get the Massey Rd properties done in time.
"The insulation guys are so busy at the moment," he said.
Rental owners have been scrambling to meet the July 1 deadline, but many have been made to wait because insulation companies have a huge backlog of jobs.
The Insulation Association has warned that rogue operators have sprung up as demand for insulation soared, and it urged homeowners to check their installers' credentials and experience.
MBIE said an estimated 100,000 rental properties were still not insulated when the rules came into force at the beginning of July.
The new standards, which were introduced by the previous National-led Government, aimed to create healthier living conditions for the 600,000 New Zealand households living in rentals across the country.
According to former Housing Minister Phil Twyford, up to 200,000 rentals did not have ceiling or underfloor insulation previously, while Ministry of Health research found 6000 children went to hospital each year with respiratory and other "housing-sensitive" conditions.
Further minimum standards for heating, ventilation and drainage will come into force for rental properties in mid-2021, and landlords will have to comply within 90 days of any new tenancy.