The interest in the structure of ice-rich planetary bodies, in particular the differentiation between ice and rock, has grown due to the discovery of Kuiper Belt objects and exoplanets. We thus carry out a parameter study for a range of planetary masses M, yielding radii 50 2 R 2 3000 km, and for rock to ice mass ratios between 0.25 and 4, evolving them for 4.5 Gyr in a cold environment, to obtain the present structure. We use a thermal evolution model that allows for liquid and vapor flow in a porous medium, solving mass and energy conservation equations under hydrostatic equilibrium for a spherical body in orbit around a central star. The model includes the effect of pressure on porosity and on the melting temperature, heating by long-lived radioactive isotopes, and temperature-dependent serpentinization and dehydration. We obtain the boundary in parameter space (size, rock content) between bodies that differentiate, forming a rocky core, and those which remain undifferentiated: small bodies, bodies with a low rock content, and the largest bodies considered, which develop high internal pressures and barely attain the melting temperature. The final differentiated structure comprises a rocky core, an ice-rich mantle, and a thin dense crust below the surface. We obtain and discuss the bulk density-radius relationship. The effect of a very cold environment is investigated, and we find that at an ambient temperature of ∼20 K, small bodies preserve the ice in amorphous form to the present.