Intracellular thermometry has recently demonstrated temperatures in the nucleus, mitochondria, and centrosome to be significantly higher than those of the cytoplasm and cell membrane. This local thermogenesis and the resulting temperature gradient could facilitate the development of persistent, self-organizing convection currents in the cytoplasm of large eukaryotes. Using 3-dimensional computational simulations of intracellular fluid motion, we quantify the convective velocities that could result from the temperature differences observed experimentally. Based on these velocities, we identify the conditions necessary for this temperature-driven bulk flow to dominate over random thermal diffusive motion at the scale of a single eukaryotic cell. With temperature gradients of the order 1°C and diffusion coefficients comparable to those described in the literature, Péclet numbers ≥ 1 are feasible and permit comparable or greater effects of convection than diffusion in determining intracellular mass flux. In addition to the temperature gradient, the resulting flow patterns would also depend on the spatial localization of the heat source, the shape of the cell membrane, and the complex intracellular structure including the cytoskeleton. While this intracellular convection would be highly context-dependent, in certain settings, convective motion could provide a previously unrecognized mechanism for directed, bulk transport within eukaryotic cells.