Firefighters were called to the Clyde St property at 6.17am on Saturday and found the house well ablaze.
A Givealittle page has been set up for Fehoko and Ana Otunuku, who with their three children, and Ana’s sister and son, lost everything in the blaze.
The family "escaped with only the clothes on their back".
The page, set up by Ana’s sister-in-law Hannah Talanoa, said the family bought the house two years ago, and the fire was "a devastating loss".
"Thankfully they do have insurance."
The family wanted to thank the wider Oamaru community for their support, generosity and compassion.
"We would like to extend our thanks to the fire, ambulance and police for their tireless efforts during this time."
Funds raised will be used to help the family purchase necessities for a new home.
Fire and Emergency New Zealand fire investigator Mark Bredenbeck said the fire was "most likely" caused by a child’s bunk bed covering a plug for a heater, he said.
"It’s possibly caused either the plug to become dislodged and spark, or it’s created some heat that has built up and started the fire that way."
He warned against putting furniture too close to any plug, to avoid similar events occurring.