We report results of a molecular dynamics simulation study of the high-temperature pyrolysis of polyethylene (PE) and the mechanical and thermal properties of the resultant carbonaceous char. The microstructure of pyrolyzed PE samples was monitored during the simulation. Mechanical properties of the resultant char were studied for char samples with varied microstructure (average coordination number and ring-size distributions) to establish structure-property relationships between mechanical (thermal) response properties and microstructure. We found that this relationship can be established based upon the random network theory of amorphous media, if additional topological constraints due to rings are taken into account. Thermal conductivity of pyrolytic char is investigated for samples with different microstructures for a wide range of temperatures. Similar to the mechanical response, the thermal response properties are correlated to microstructure. It is shown that the behavior of the thermal conductivity can be well described by Einstein's heat transfer theory, if microstructure effecs are taken into account.