A crowdfunder page has been set up in honour of the twin three-year-old girls who died in a Batlow house fire on Monday.
Within 12 hours of going live, the GoFundMe reached and exceeded its $2000 target.
Organisers say the funds will go towards replacing belongings lost to the mother and six-year-old brother after the house was destroyed.
It comes after Police Strike Force Edmondson was formed to investigate.
Riverina police detective Superintendent Bob Noble said the cause of the fire was still yet to be established, but warned the community against the intentional or unintentional spreading of rumours.
"There was a fireplace in the dwelling, it was burning as I understand it and is understandable on a cold day in an alpine area of the state," Superintendent Noble said.
"We will be looking at all possible sources of ignition. In a dwelling, there are many."
Superintendent Noble did not disclose where in the house the three-year-old twins were found by first responders.
Firefighters arrived at the scene after 11am on Monday, and attempted to rescue the girls from the burning building.
"I just want to make it very clear that we're keeping an open mind in respect to the nature of this incident," Superintendent Noble said.
"What we obviously have is two young children that have died, we can't speak to them so there are two sources of information that are not available to us."
Police will continue to canvas witnesses, including the parents of the three-year-old children, the six-year-old brother, and neighbours.
In the wake of the death of the three-year-old twins, Superintendent Noble appealed to the community to avoid inadvertently spreading "unhelpful rumours" around the community.
"In a devastating tragedy such as this, rumour, innuendo, speculation and conjecture surrounds, it's very unhelpful," Superintendent Noble said.
"We need to deal in evidence and facts, and facts can't be ascertained without checking and multi-sourcing, and that's what our police will do."
The deaths came just days after a fatal crash in Tumut took the lives of a pregnant mother's unborn child and her 10-year-old daughter.
Superintendent Noble said that mental health provisions and counselling will be offered to the community.
"It's a community that's been through devastation recently in terms of the bushfires," Superintendent Noble said.
"Many homes were already destroyed earlier this year in those bushfires.
"The people of Batlow are doing it very hard, no doubt this particular family are devastated."