Context. Thermal inertias of atmosphereless icy planetary bodies happen to be very low. Aims. We relate the thermal inertia to the regolith properties such as porosity, grain size, ice form and heat transfer processes to understand why it is low. We interpret the dichotomy in thermal inertia of the surface of Mimas in terms of changes in regolith properties. We predict how the thermal inertia of these bodies may vary with heliocentric distance depending on these properties. Methods. We combine available models of conductivity by contact or radiation to understand what heat transfer process is predominant.Results. The magnitude of the thermal inertia of a porous icy regolith is mainly governed by the crystalline or amorphous ice forms, and the quality of contacts between grains. Beyond the orbit of Jupiter, thermal inertias as low as a few tens J/m 2 /K/s 1/2 are difficult to reproduce with plausible porosity and grains sizes made of crystalline ice unless contacts are loose. This is, on the contrary, straightforward for regoliths of sub-cm-sized grains made of amorphous water ice. This study points out the importance of including the temperature dependence of thermophysical properties of water ice forms and the radiative conduction in thermal models of these bodies. The relatively high thermal inertia of the leading face of Mimas can be explained by a regolith of crystalline ice grains in tight contacts, which are eventually sintered by the bombardment of high energy electrons. The low thermal inertia of its trailing face is easily reproduced by a regolith of moderate porosity with sub-mm-sized grains of amorphous ice. The characteristic decrease of thermal inertia with heliocentric distance of icy atmosphereless surfaces and the very low thermal inertia of relevant trans-Neptunian objects are easily explained if amorphous ice is present at cm depths below a thin layer of crystalline ice.