Tulio Ayala, 34, and 31-year-old Maria Ayala are now charged with multiple counts of endangering the welfare of a child.
Police say the couple's four kids, ages 4 to 15, were left at their home in Central Islip for six days without food or heat.
The children used a small space heater and a gas oven to keep them warm.
They are now in a relative's care.
The Central Islip school district contacted authorities. The couple was arrested Wednesday.