Six-year-old Isaiah Sammon and 2-year-old Evian Young are doing well after they were saved by their father, but three other children, 7-month-old Jayden, 3-year-old Alexis and 4-year-old Dasani Young died in the blaze Wednesday night.
Fire officials say a space heater is likely to blame.
The children's grandmother says their mother had tried to get heat for their apartment.
"When it was cut off she went to the Salvation Army, put money into account to have it paid up and it wasn't enough," Stephanie Pittman said. "I don't understand why. They had a disabled child, give them a break."
The children's father, 27-year-old Andre Young, remains in critical condition with injuries he suffered trying to rescue his children.