Numerical simulations of convection in a wide domain with spatially varying internal heating intended to mimic tidal dissipation in Io's proposed asthenosphere are performed in order to better understand the convective dynamics and, in particular, to quantify the relationship between surface observables (particularly the distribution of heat flux) and tidal dissipation. Two-dimensional calculations at high internal heating Rayleigh number RaQ of up to 1010 indicate a mean, domain-wide flow with superimposed small-scale instabilities. The mean flow spreads out the tidally-dissipated heat, resulting in long-wavelength surface heat flux variations that decrease in proportion to RaQ-0.21. This scaling is shown to apply to different domain widths and also to three-dimensional geometry. Powerlaw scalings are also obtained for velocities and temperatures. These mean flow scalings are also derived analytically. Scaling to Io's asthenosphere, long-wavelength heat flux variations of order several percent are predicted, with temperature variations of order tens of Kelvins and mean flow velocities of 50--5600 m.yr-1. ¿ 2001 American Geophysical Union