Recently Brown et al. (1991) showed that Triton's internal heat source could amount to 5–20% of the absorbed insolation on Triton, thus significantly affecting volatile transport and atmospheric pressure. Subsequently, Kirk and Brown (1991a) used simple analytical models of the effect of internal heat on the distribution of volatiles on Triton's surface, confirming the speculation of Brown et al. that Triton's internal heat flow could strongly couple to the surface volatile distribution. To further explore this idea, we present numerical models of the permanent distribution of nitrogen ice on Triton that include the effects of sunlight, the two‐dimensional distribution of internal heat flow, the coupling of internal heat flow to the surface distribution of nitrogen ice, and the finite viscosity of nitrogen ice. From these models we conclude that: (1) The strong vertical thermal gradient induced in Triton's polar caps by internal heat‐flow facilitates viscous spreading to lower latitudes, thus opposing the poleward transport of volatiles by sunlight, and, for plausible viscosities and nitrogen inventories, producing permanent caps of considerable latitudinal extent; (2) It is probable that there is a strong coupling between the surface distribution of nitrogen ice on Triton and internal heat flow; (3) Asymmetries in the spatial distribution of Triton's heat flow, possibly driven by large‐scale, volcanic activity or convection in Triton's interior, can result in permanent polar caps of unequal latitudinal extent, including the case of only one permanent polar cap; (4) Melting at the base of a permanent polar cap on Triton caused by internal heat flow can significantly enhance viscous spreading, and, as an alternative to the solid‐state greenhouse mechanism proposed by Brown et al. (1990), could provide the necessary energy, fluids, and/or gases to drive Triton's geyser‐like plumes; (5) The atmospheric collapse predicted to occur on Triton in the next 20 years (Spencer, 1990) may be plausibly avoided because of the large latitudinal extent expected for permanent polar caps on Triton.