The deceased children were all under the age of 10, New Albany Fire Marshal Chris Koehler said.
A fourth child was severely injured in the blaze, and two adults -- including the mother of the four children -- were at the scene when the fire began Saturday, the Louisville Courier-Journal reported.
"The whole family's hurting," family member Lee Lipford said. "Everybody loved those kids like they were their own kids."
The children were found in the home's front room after the fire was contained.
The room was gutted, and the rest of the three-bedroom home sustained major heat and smoke damage.
Investigators said they have sent the heater to a lab to rule out the possibility of an electrical problem.
The cause of the fire is still under investigation.
Swim Week Miami Beach 2014 [PHOTOS]