The family's spokesperson says the L.A. County Coroner found the 38-year-old restaurateur was suffering from coronary artery disease and also had a "mildly enlarged heart."

The family says another doctor confirmed for them that Harry had calcification in 3 of his main arteries ... which caused a sudden cardiac arrest.

TMZ broke the story, Harry -- son of Hard Rock founder Peter Morton -- was found unresponsive this past Saturday at his Beverly Hills home. He was pronounced dead at the scene.

We're told the Coroner's Office is still conducting further testing on Harry's other organs, and will issue the official cause of death once those are completed.