1) In Dr. Heidegger's Experiment, the eponymous doctor tests four of his acquaintances by offering them water from a river in Florida near the Fountain of Youth. This supernatural element is the most central gothic pattern in the short story. More specifically, there is the presence of something esoteric (the elixir of youth) which breaks the bounds of ordinary mortality.
2) It is also interesting that the Fountain of Youth is to be found in Florida rather than some more exotic locale. This is yet another feature of gothic literature, particularly in the time of Hawthorne. Indeed, Hawthorne himself once remarked:
In truth it is desperately hard work when we attempt to throw the spell of hoar antiquity over localities with which the living world and the day passing over us have aught to do. ("Howe's Masquerade")
The legend of the Fountain of Youth is an ancient one and, in localizing it near Lake Macaco in Florida, Hawthorne is indeed investing it with gothic romance by throwing the "spell of hoar antiquity" over it.
3) The setting is also an important aspect of gothic literature. In traditional gothic writings, the setting was usually mysterious or sinister in some way and locales like castles were often favored. Here, we must look to the author's description of Dr Heidegger's study:
It was a dim, old-fashioned chamber, festooned with cobwebs, and besprinkled with antique dust. Around the walls stood several oaken bookcases, the lower shelves of which were filled with rows of gigantic folios and black-letter quartos, and the upper with little parchment covered duodecimos.
4) The presence of witchcraft is a gothic element that can also be found in quite a few of Hawthorne's works, and "Dr. Heidegger's Experiment" is no exception. We are told of a "ponderous folio volume, bound in black leather, with massive silver clasps" that is, although this isn't obvious from the outside, a book of magic. We know it is a sinister work of magic because once, when a chambermaid tried to dust it:
the skeleton had rattled in its closet, the picture of the young lady had stepped one foot upon the floor, and several ghastly faces had peeped forth from the mirror; while the brazen head of Hippocrates frowned, and said,—"Forbear!"
Indeed the paragraph after the doctor's friends enter his study is full of gothic elements—the study has an array of gothic paraphernalia, from the enchanted mirror and the (possibly magical) portrait of a lost love to a skeleton in the oak closet and the book of magic. It is a very short story that nonetheless contains many stock gothic elements. However, it is Hawthorne's treatment of the gothic that is remarkable because it is not merely a gothic short story but rather a story that employs gothic elements in order to convey a parable by means of light satire.