A police investigation found that the heater had been switched on
Susan Gould, 55, was dragged under the wheels of the 4×4 when she leaned into the car and turned on the ignition without realising it was in third gear.
Mrs Gould was run over when the car shot forward 11 metres (36ft) while she defrosted it in Hayton, near Retford, Nottinghamshire, on November 29 last year.
Paramedics dashed to the pub car park where the accident happened but she had suffered major chest injuries and was pronounced dead at the scene.
A pathologist told an inquest into her death that she would have become unconscious "almost immediately and there was no prolonged suffering."
A police investigation found that the heater had been switched on and air vents turned towards the windows.
CCTV covered the car park and this showed Mrs Gould, from Sutton-cum-Lound, Notts., walking to the car, leaning through the open driver's door.
Forensic collision investigator, PC Dave Abbott said: "There was a covering of frost on the car park surface and likewise on the vehicle.
"The windows were frosted, the car was covered in frost.
A police investigation found that the air vents were turned towards the windows
It must still be incredibly shocking and traumatic for all of you
"She leans in and very shortly afterwards the vehicle moves forward.
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"We know it had been started and the vehicle moved off.
"Because of the extra electrical energy needed to power the heater, this would make the engine work a little harder.
"Being a cold morning, the engine works harder.
"You would note things like higher engine revs.
"It would be revving slightly higher than on a nice warm day.
"That would cause it to propel itself more than normal".
Nottinghamshire senior coroner Mairin Casey said Mrs Gould had been planning to make the school run to help her daughter, who gave birth the day after the tragedy.
Recording a verdict of accidental death she said: "This was an accident in the truest sense, a random event which could not have been foreseen."
"I offer my most sincere condolences.
"It must still be incredibly shocking and traumatic for all of you."
A verdict of accidental death was recorded.