Radioactive heating is the main energy source of comets residing in the distant parts of the Solar System. It should determine whether liquid water could have existed in comets and whether comets, presumably formed of amorphous ice, could have retained the ice, at least partly, in this pristine form. Thermal evolution calculations of relatively large (over 10 km in radius), porous comet nuclei are performed for many different initial parameter combinations. The radioisotopes considered are 40K, 232 Th, 235U, and 238U, in meteoritic abundances, as well as 26Al, in various initial abundances. We allow for heat conduction through the ice-dust matrix, as well as advection by flowing gases. Crystallization of the amorphous ice accompanied by release of occluded gases, and sublimation/condensation from/ onto the pore walls are taken into account. We find that porous comet nuclei may emerge from the long-term evolution in three different configurations, depending on the thermal conductivity, porous structure, radius, etc.: (a) preserving their pristine structure throughout; (b) almost completely crystallized (except for a relatively thin outer layer), and (c) having a crystallized core, a layer of frozen gas (originally occluded in the amorphous ice) and an outer layer of unaltered pristine material. Liquid cores may be obtained only if the porosity is negligible. The extent of such cores and the length of time during which they remain liquid are again determined by initial conditions, as well as by physical properties of the ice. If, in addition to the very low porosity, the conductivity were extremely low, it should be possible to have both an extended liquid core, for a considerable period of time, and an outer layer of significant thickness that has retained its original pristine structure.