In the Part 1 paper (Gawin, et al. 2005) some experimental results concerning micro-structural tests, permeability measurements and stress-strain tests of four types of High Performance Concrete, exposed to elevated temperatures (up to $700^{circ}C$) are presented and discussed. On the basis of these experimental results parameters of the constitutive relationships describing influence of damage and temperature upon material intrinsic permeability at high temperature were determined. In this paper the effects of various formulations of damage-permeability coupling on results of computer simulations are analysed and compared with the results obtained by means of the previously proposed approach, that does not take into account the thermo-chemical concrete damage directly. Numerical solutions are obtained using the recently developed fully coupled model of hygro-thermal and damage phenomena in concrete at elevated temperatures. High temperature effects are considered by means of temperature and pressure dependence of several material parameters. Based on the mathematical model, the computer code HITECOSP was developed. Material parameters of the model were measured by several European laboratories, which participated in the "HITECO" research project. A model problem, concerning hygro-thermal behaviour and degradation of a HPC structure during fire, is solved. The influence of two different constitutive descriptions of the concrete permeability changes at high temperature, including thermo-chemical and mechanical damage effects, upon the results of computer simulations is analysed and discussed.