For the first time the role of the internal heat source, due to radioactive decay in Triton's core, is investigated with respect to geyser-like plumes. Triton is one of only three known objects in the Solar System (the other two are Earth and the jovian satellite Io) where eruptive activity has been definitely observed. A new mechanism of energy supply to the Tritonian eruptive plumes is proposed. This mechanism is based on heat transport in the solid-nitrogen polar caps due to thermal convection, in addition to conduction. The conductive-convective model shows that a 1 K increase in the N-2 ice subsurface temperature over the surface value is reached much closer to the surface in the region of an upwelling subsurface plume compared with a pure conductive case. This temperature rise is sufficient to double the nitrogen vapor pressure. Therefore, it is enough to drive the atmospheric plumes to the observed height of approximate to 8 km, provided 1 K warmer nitrogen ice encounters a vent and hence is exposed to the approximate to 15-mu bar Tritonian atmosphere. Solid-state convection onsets if a nitrogen layer is sufficiently thick and the average solid N-2 grain size is small enough. Critical values of these parameters are presented for Triton. A possible origin of the subsurface vents on Triton is also suggested. (C) 1997 Academic Press