We assess local-time variations of epithermal-neutron count rates measured by the Lunar Prospector Neutron Spectrometer. We investigate the nature of these variations and find no evidence to support the idea that such variations are caused by diurnal variations of hydrogen concentration across the lunar surface. Rather we find an anticorrelation between instrumental temperature and epithermal-neutron count rate. We have also found that the measured counts are dependent on the temperatures of the top decimeters of the lunar subsurface as constrained by the Lunar Reconnaissance Orbiter Diviner Lunar Radiometer Experiment temperature measurements. Finally, we have made the first measurement of the effective leakage depth for epithermal-neutrons of ~20 cm.