Least squares Maxwellian fits have been made to the data from the Apollo 15 suprathermal ion detector experiment (side) while the dusk magnetosheath at lunar orbit. It is found that the data are best fit by superimposing two co-moving proton populations whose temperatures differ radically: kT ~ 10 eV and kT ~ 100 eV. This two-temperature distribution cannot be explained by alpha particles. The higher temperature population is typical of that expected for the fully shocked magnetosheath at lunar distances. The colder distribution could arise from cold plasma from within the magnetosphere brought up to magnetosheath flow speeds, but it is more probably due to unshocked solar wind.