Updated 6.20pm: A coroner has found living in a cold state house may have contributed to the death of an Auckland toddler.

Two-year-old Emma-Lita Bourne died last year from a brain haemorrhage, following a battle with bronchial pneumonia.

A coroner's inquiry has found the girl's cold living conditions may have contributed to her pneumonia.

Housing New Zealand had installed a ventilation system and electric heater in the girl's home, but her family couldn't afford to use it.

The coroner also found medical professionals did they all they could to save the girl.

Children's Commissioner Russell Wills said her death was an "entirely preventable" and frustrating tragedy:

"The odds are, if she was living in a warm dry house, she wouldn't have got pneumonia and she wouldn't have died."

And Green co leader Metiria Turei said it wass a classic case of why state houses should have to meet a warrant of fitness test. Her view is that the offer of a heater was inadequate.

"Giving a family like that a heater and expecting them to even be able to pay the power bill is simply ridiculous. The homes themselves need to be warm and dry and safe for our kids."

Housing Minister Nick Smith said the Government last year gave top priority to families with rheumatic fever and has also taken other moves.

"The government has moved to insulate more than 300,000 homes, including every state house the can be insulated."

But Russell Wills argues 70% of children living in poverty are in private rentals so the solution needs to apply to both:

"If we had a warrant of fitness in place for both Housing NZ and private rentals, many fewer children would get sick, and fewer children would die."

The report comes as a new study into the effects of poor rental housing on children can be the tipping point for housing warrants of fitness.

Otago University professor Philippa Howden-Chapman has been given a $5 million grant by the Health Research Council to help improve rental houses for the sake of children's health.

"People say, 'if you have a new standard, landlords will just exit and people will be homeless." We don't think that's what's going to happen."

She'll be working with a handful of local councils to assess the viability of a rental WOF.