This study investigates the detectability of a putative layer of regolith containing water ice in the lunar polar regions using ground penetrating radar (GPR). Numerical simulations include realistic variations in the relative permittivity of the lunar regolith, considering both density and, for the first time, the effects of temperature on permittivity profiles. We follow the case of previous theoretical studies of water migration, which suggest that water ice accumulates at depths ranging from a few centimeters to tens of centimeters, appropriate depths to explore using GPR. In particular, frequency-modulated continuous wave (FMCW) radar is well-suited for this purpose due to its high range resolution and robust signal-to-noise ratio. This study evaluates two scenarios for the presence of lunar water ice: (1) a layer of regolith containing water ice at a depth of 5 cm, with a thickness of 5 cm, and (2) a layer of regolith containing water ice at a depth of 20 cm, with a thickness of 10 cm. Our computational results show that FMCW GPR, equipped with a dynamic range of 90 dB, is capable of detecting reflections from the interfaces of these layers, even under conditions of low water ice content and using antennas with low directivity. In addition, optimized antenna offsets improve the resolution of the upper and lower interfaces, particularly when applied to the surface of ancient crater ejecta. This study highlights the critical importance of understanding subsurface density and temperature structures for the accurate detection of water-ice-bearing regolith layers.