Whether or not the eerie elements of "Dr. Heidegger's Experiment" are actually supernatural is subject to debate. It's a question of theatrical showmanship vs. genuine superstitious belief. The theme creates a mood of doubt and forces the reader to ask some difficult questions about the nature of reality – at least as defined within the narrative. It also severely complicates our understanding of the title character, who has at least one foot in a sinister, supernatural realm.
Hawthorne condemns Dr. Heidegger for playing God.
Dr. Heidegger's character is both venerable and Godly. Hawthorne paints him as an admirable, if other-worldly, figure.