The first obituaries and reports gave no cause of death; well, that was last month. It is now a few weeks later. The more recent reports are saying that a heart attack was the cause of death, and suggesting that it must have happened quickly and relatively easily.

He was not well anyway. He was a recent widower, and one of the online eulogies insists that he died of a broken heart, following the loss of his wife. His diabetes was a thing to contend with. He also suffered from shingles, badly, and he had had spinal surgery within the past five years.

More:

http://bangordailynews.com/2016/04/03/news/jim-harrison-prolific-autho-and-an-outdoorsman-dies-at-78/

Doug Peacock, in The Daily Beast:
http://www.thedailybeast.com/articles/2016/04/02/jim-harrison-and-the-art-of-friendship.html