Gallium phosphide (GaP) is an attractive candidate for wide-bandgap solar cell applications, possessing the largest bandgap of the III-arsenide/phosphides without aluminum. However, GaP cells to date have exhibited poor internal quantum efficiency (IQE), even for photons absorbed by direct transitions, motivating improvements in material quality and device structure. In this work, we investigated GaP solar cells grown by molecular beam epitaxy over a range of substrate temperatures, employing a much thinner emitter than in prior work. Higher growth temperatures yielded the best solar cell characteristics, indicative of increased diffusion lengths. Furthermore, the inclusion of an AlGaP window layer improved both open-circuit voltage and short wavelength IQE.