Flight 3606 turned back over Idaho and flew back to Seattle-Tacoma International Airport to return the heart, which should have been taken off a previous flight on December 9.
Southwest didn't provide the name of the company that shipped the heart, but confirmed that it specialized in shipments that are "life critical", the Times reported. Or if it made it there in time for a likely transplant.
The heart, which had been on an earlier flight from Sacramento to Seattle, was not removed from the plane as it should have been.
Apparently, someone had forgotten to unload a human heart, The Seattle Times reports.
Southwest did not reveal the intended destination of the heart, or what it was being used for, thus impossible to tell if anyone's life was ever in danger.
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Oakland City Councilman Larry Reid sits on also sits on the Joint Powers Authority board. "So, the fight is ours". I know Mark [Davis, the Raiders owner] has expressed it. "But when that time comes, we will enjoy it".
Following the flight's return to Seattle, the heart was taken to a donor health centre for tissue storage and was said to have been received within the required time frame, the newspaper added.
"Once we realized the error we immediately worked to return to Seattle", airline spokesman Dan Landson told French news agency AFP. But the shock gave way to kindness, and many onboard were "happy to save a life".
LifeCenter Northwest organizes the transfer of transplant organs in the region.
According to the Seattle Times, Dr Gottschalk said passengers were anxious about whether the heart would still be viable for transplant. "There's a time limit to get where it needs to go".
Dr. Andrew Gottschalk, who was onboard the delayed flight, described the incident as a "horrific story of gross negligence". The United Kingdom clinical guidelines recommend a maximum of 6 hours.