A friend, Makailah Stehlin, said people shouldn't criticise Ms Namana for leaving her children for "a split second or longer" because they don't know what she was going through.
Police say they've told Child, Youth and Family of the incident and are yet to interview the mother.
The central regional director of CYFS, John Langley, said this "tragic event" showed what could happen if babies and young children were left without adequate supervision.
"We would advise anyone who comes across children left without adequate supervision to call the police. When we are alerted to children being left unsupervised, we ensure the immediate safety of the children and work with the parents and wider family to ensure adequate arrangements are made in future."
It's understood CYFS hasn't had recent involvement with this family but has had in previous times.
Investigators have found a cigarette lighter in the vehicle but police couldn't confirm that it began the fire.
A witness told the Herald people at the scene who had rushed to help the toddlers had established one had found a lighter and accidentally set the back of the driver's seat on fire.
Police praised the actions of the people who helped pull the children from the car and applied first aid.
Ms Namana also thanked the rescuers and the emergency services for their prompt response in a statement from Waikato Hospital.
Mutu Ngarimu, who runs a business beside the Gladstone Rd carpark, saw the burning car and rushed out with a fire extinguisher.
It was not until the fire was out that Mr Ngarimu noticed a child in the car.
"There was a little girl in there, so I pulled her out and a member of the public performed CPR on her," he told the Herald.
"I went back into the vehicle to see if anyone else was in there and that's when I noticed the 22-month-old in there, so I pulled him out and he was unconscious."
Two men working across the road at Firestone Tyres also dashed to help. Manager Scott Brocket said he used a fire extinguisher to help put out the blaze. A builder working on the store's roof helped Mr Ngarimu pull the children from the car.