Branz researcher Vicki White said the "distinct lack of heating" was of concern.
"The WHO recommends a minimum of 18 degrees in any occupied areas. Those unheated rooms are likely to be quite a lot colder than that."
Paediatrician professor Innes Asher said people were falling ill - even dying - because of illness related to living in temperatures of just 8-12C.
"It's not just that you don't feel very good, you can die from it."
She highlighted the case of 2-year-old Emma-Lita Bourne whose cold, damp state house was identified as a contributing factor to her death in a 2015 coroner's report.
One single mother, of a 3-year-old son, knows too well the impact the cold can have on health.
The woman, who has chosen to stay anonymous, puts sheets over doors and under door frames in an effort to stop the cold air getting into their bedrooms.
The 26-year-old and her 3-year-old son moved into an "older-style" rental that has no insulation. Both have been sick ever since.
It costs her about $100 a fortnight in wood, paper and fire-starters to light the open fireplace in the house, which had no other heating options.
She said it was not enough to heat the three-bedroom house.
"As a mum I was completely heartbroken knowing how cold this home was is the reason my son had this cold he could not shake off."
The Branz report found dampness and mould were more prevalent in rental homes, with 56 per cent of these showing mould - compared to 44 per cent of owner-occupied homes.
Mould was most common in bathrooms, and in 20 per cent of living areas and bedrooms.
In rentals the situation was worse - almost 30 per cent had visible mould in bedrooms, compared to 18 per cent in owner-occupied houses.
Many renters (38 per cent) also did not have access to cost-effective heating appliances, such as heat pumps, wood burners, and flued gas heaters, compared to just 12 per cent of homeowners who went without.
Instead renters were more reliant on portable heaters, which the report said were typically more expensive to run and less effective.
Asher said the findings highlighted the importance of the Healthy Homes Guarantee Bill passed into law, which passed its second reading in Parliament last week.
It needs to pass a third reading, and be given the royal assent, to be passed into law but, if passed, would see landlords forced to abide by specific standards requiring a warm, dry property.
Branz researcher Vicki White said insulation and heating were essential for a warm, dry house and ensuring a healthy environment.
"Houses kept warm and dry with good levels of insulation, good ventilation systems, such as extractor fans and regularly opened windows and doors will help reduce the risk of damp and mould."
However, the report, jointly funded by the Building Research Levy, MBie and the Energy Efficiency and Conservation Authority, found that although most homes had some level of insulation it was generally "suboptimal" and there was a need for more effective ventilation.
Branz researcher Mark Jones said it was unlikely the identified issues would surprise anyone but the report gave strong empirical evidence as to the size of the problem.
"One of the most important aspects of that, is not just what we report, but how will organisations use this data as well."
