Although it is hard to say for Quảng Đức specifically, it wouldn't be without any precedent, a famous similar case is that of Percy Shelley's heart, Mary Shelley's, his wife, carried the heart with her for the longest time.
One of the most prominent hypothesis is that it was due to tissue calcification from a previous tuberculosis infection he had. Unfortunately, it seems both cases lack the analysis of an expert, allowing debate on whether it is indeed the heart, or perhaps some other body part, that survived the fire, the liver being one popular choice among anatomists.
Despite having no expert analysis, there are multiples accounts of the survival of Percy's "heart". One quote from a 1955 The Journal of the History of Medicine by Arthur Norman found in a 1995 New York Times letter reads:
[Shelley may have suffered from] a progressively calcifying heart . . . which indeed would have resisted cremation as readily as a skull, a jaw or fragments of bone.
Another evidence can be found in an 1822 manuscript by Leigh Hund and Edward Trelawny titled "Account of the death and cremation of Percy Bysshe Shelley, together with a description of his life and character and that of his companion Captain Williams, who was drowned with Shelley in his yacht"
It is a curious circumstance that the heart, which was unusually large, together with some other vessels in that quarter(?) seemed almost proof against fire, for it was still entire in figurine & apparently in substance, though the intensity of the heat was so great that harder substances were reduced to white dust.
(Quote taken from folio 18)
Whatever may've been the actual reason/body part in either case, it is at least reasonable to believe the stories to be true without relying purely on some supernatural phenomenon.