Dr. Heidegger is a cryptic fellow – but that's part of his charm. For starters, we don't know if he's a dear old doctor or a seriously cynical scientist playing the experimentalist on his friends at their expense. We make a decent argument for each one under "Character Roles," but the short version is that, on the one hand, he's the wise protagonist who contrasts with his foolish guests, while, on the other hand, he's got a dark history (skeletons in the closet, both literal and figurative, a dead fiancée, lots of dead patients) with no justification or explanation. This ambiguity is par for the course, however – nearly all of "Dr. Heidegger's Experiment" is open to interpretation.
One of the big questions that arises in thinking about Dr. Heidegger is what kind of doctor he is. One answer is that he is a physician or medical doctor. We figure that he treats sick people because many of his former patients are dead, and we know that he prescribes drugs because his fiancée died from taking one of his prescriptions (exactly how or why is, expectedly, not clear). But he's also a scientist of sort – we know he runs experiments pretty regularly (his guests expect something involving a dead mouse or a microscope). Lastly, Dr. Heidegger is a philosopher. His interests with this particular experiment are moral and psychological – not physiological or chemical. In sum, he's a doctor of many sorts. It's fitting, then, that Dr. Heidegger keeps the bust of Hippocrates in his study – more on that in "Symbols, Imagery, Allegory."
The mystery surrounding Dr. Heidegger's character has a lot to do with the general atmosphere of the story. Whether or not he's a good doctor, exactly what kind of doctor he is, what his motives are in running this "experiment," and the big one – whether or not the elixir is real – are what makes "Dr. Heidegger's Experiment" such an interesting read.