Thomas Mann died on August 12, 1955, at the age of 80, of a vascular cause: the rupture of a major artery in the abdomen, and not cancer. The sources agree on the type of problem, but describe somewhat differently which artery it was and the mechanism.
On July 18, 1955, while on vacation in Noordwijk, in the Netherlands, he felt pain and swelling in his left leg. The doctors diagnosed thrombophlebitis (inflammation of a vein with a clot). Taken to a hospital in Zurich, he went into shock and died weeks later.
According to the English-language Wikipedia, the autopsy showed that the diagnosis had been wrong: there had been the rupture of an aneurysm of the iliac artery, with a large hematoma behind the abdominal cavity and compression and thrombosis of the iliac vein. The German-language Wikipedia speaks of a rupture of the lower part of the abdominal aorta as a consequence of arteriosclerosis, and the Portuguese-language Wikipedia summarizes the cause as an aneurysm. He was buried on August 16, 1955, in the cemetery of Kilchberg, near Zurich.
Sometimes one hears that Mann died of lung cancer, but none of the sources consulted points to this as the cause of death. The Historical Dictionary of Switzerland records the death in Zurich or Kilchberg, without giving the cause.