The problem of rarefied-gas heat transfer between parallel plates is treated by a Monte Carlo procedure. Hard-sphere molecule collisions are assumed. The distributions of target molecules are assumed to be locally Maxwellian, with thermal velocity and density varying across the channel. The temperature, density, and heat transfer are found for flow conditions ranging from Knudsen numbers of 0.05 to the free-molecule regime for a wall-temperature ratio of 1 to 4. The present results were compared with the results of another Monte Carlo solution obtained by using a different method and were found to agree with those results; they were also compared with other analytical solutions. The present results also agreed with the results obtained from a continuum solution with slip boundaries except that the continuum conductivity was too high for the larger Knudsen number cases.