...a piece of fissile material...
No. A small lump of the same kind of "fissile material" that is used to fuel nuclear power stations will just sit there for many thousands of years without giving off any appreciable heat. If you want it to make heat, then you'd have to create the conditions for a nuclear chain reaction, which would require (among other things) more of it than you could fit into a coffee cup.
Also, you would receive a lethal dose of radiation standing anywhere near a nuclear chain reaction for more than a few seconds.
On the other hand, you might be interested in reading about radioisotope thermal generators (RTGs). They operate on the decay heat from a highly radioactive source, and AFAIK, there is no theoretical minimum size. Some sources can generate a lot of heat, but at the same time, the ionizing radiation they produce is relatively low energy, such that they require much less shielding than a fission reactor.
On the gripping hand, there's what @controlgroup said: Ingesting any amount of any radioactive substancecontamination (especially from an alpha source) can be extremely bad for your health. Don't chance ittake chances with that stuff!