Another 800 of the jets have been ordered by airlines across the globe, including 24 by British Airways and 16 by Virgin.
Footage of the Ethiopian Airlines Dreamliner showed fire damage on the roof at the rear of fuselage.
Nobody was on board the plane, which was parked at the time and was not preparing to take-off or land. Heathrow was closed between 4.30 and 6pm, causing delays to scores of flights and travel chaos for thousands of passengers after some flights were diverted. In January a battery on an unoccupied Dreamliner flight operated by Japan Airlines burst into flames after landing at Boston airport.
The following week safety regulators in Europe, America and Asia banned the plane from taking off after another Dreamliner was forced to make an emergency landing following fears over its lithium ion batteries.
In April an Ethiopian Airlines Dreamliner - said to be the plane involved in the Heathrow incident yesterday - flew from Addis Ababa to Nairobi on the first commercial flight since the grounding.
The battery problems followed endless production difficulties for the Dreamliner, which was hit by a series of incidents including two fuel leaks, brake problems and a fire.
The jet has been marketed as a quiet, fuel-efficient aircraft carrying up to 290 passengers on medium-range routes.
It boasts a higher ceiling and bigger windows containing 'smart glass' which can dim at the touch of a button until they are completely blacked out.
It should have entered passenger service in 2008 but it was not until October 2011 that the first commercial flight was operated by Japanese carrier All Nippon Airways.
The Dreamliner is the first large passenger jet to use the lightweight lithium ion batteries on such a scale. The batteries have previously caused fires in cars, computers and mobile phones as well as small aircraft.
A spokesman for Boeing said: 'We have Boeing personnel on the ground at Heathrow and are working to fully understand and address this.'
LUXURY JET WITH A TROUBLED HISTORY
• July 28 2012: A fan shaft fails during runway tests in South Carolina
• December 2012: A Dreamliner was forced to make an emergency landing in New Orleans
• January 7 2013: an unoccupied Dreamliner flight bursts into flames at Boston airport
• January 15 2013: A flight made an emergency landing in Japan after a smoke alarm went off. The string of incidents led to regulators ordering a global grounding of the entire Dreamliner fleet, which lasted for four months
• June 2 2013: Battery-related problems were reported on a Japan Airlines aircraft forcing the airline to use an alternative plane
• June 12 2013: A flight in Japan was cancelled after one of the engines failed to start
• June 18 2013: A United Airlines flight was diverted to Seattle due to an oil-filter problem
• June 24 2013: A Dreamliner operated by United Airlines had to make an emergency landing in Denver due to a brake problem
• July 3 2013: Polish airline LOT cancelled a Dreamliner flight to Chicago because the aircraft had 'problems with the power supply'
- Daily Mail