Monte Carlo models of lunar accretion are constructed by randomly sampling mass and veloctiy distributions of objects in the solar nebula in circumsolar and circumterrestial orbits. The thermal effect of an impact is expressed as the volume of melt produced. The melt volumes produced by each Monte Carlo case are sorted into regions to produce percentage melt estimates as a function of radius. One hundred cases are calculated to obtain a range of plausible thermal histories for lunar accretion. The principal measure of heterogeneity used here is the average percentage of surface redistributed by large impacts as a function of radius of the moon: in these studies that measure was around 15%. The average melt percentage estimates show substantial deep melting, but the spread of melt percentage values about the mean from the random sampling procedure is wide enough to include 0% melting for radii below 1000 km and 100% melting for radii below 500 km. The average melt percentages about 1000 km in the moon are below 15% with small spreads about this average. The sensitivities to reasonable variations in solar nebula and geophysical parameters are investigated. No attempt is made to model heat transfer within the moon.