We have simulated the passage of heavy ions through a tungsten crystal in which the atoms are thermally displaced and the ions are subjected to a force which represents inelastic‐loss mechanisms. Semiempirical Born‐Mayer potential functions and inelastic‐loss parameters were obtained for the xenon‐tungsten and krypton‐tungsten systems. Only the xenon‐tungsten system was studied in detail. We find that below 500°K thermal displacement of the lattice atoms has little effect upon the collision dynamics for ions moving in the channel center. Energy losses to electronic processes during collisions are calculated, and the loss rates compared to the simulation loss rate parameter. Agreement is good. Simulated integral‐penetration curves agree quite well with the experimental results. A mechanism which attributes the strong temperature dependence of ranges to variations in the inelastic‐loss constants is presented and compared to experimental results.