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Fire crews were called to a burning car on the top floor of the Pentagon Centre car park in Chatham at 12.20pm on Monday.
Shopping centre staff used fire extinguishers to stop the fire spreading before firefighters arrived and extinguished the blaze.
The owner of the car, a Ford Fiesta, was not present at the time of the fire, which is thought to have been caused by an electrical fault.
Damage was restricted to the car's engine compartment.