Epitaxial thin GaN films ($60 nm) have been grown on a-plane sapphire substrates at different growth temperatures (500-700 C) using laser molecular beam epitaxy (LMBE). The effect of growth temperatures on the structural and optical properties of GaN layers grown on low temperature (LT) GaN buffer on prenitridated a-sapphire have been studied systematically. The in situ reflection high energy electron diffraction pattern revealed the three-dimensional epitaxial growth of GaN films on a-sapphire under the adopted growth conditions. The full width at half maximum (FWHM) value of x-ray rocking curves (XRCs) along GaN ( 0002) and (10-12) planes decreases with increasing growth temperature. The FWHM values of ( 0002) and (10-12) XRC for the 700 C grown GaN film are 1.09 and 1.08 , respectively. Atomic force microscopy characterization showed that the grain size of GaN increases from 30-60 to 70-125 nm with the increase in growth temperature as GaN coalescence time is shorter at high temperature. The refractive index value for the dense GaN film grown at 600 C is obtained to be $2.19 at the wavelength of 632 nm as deduced by spectroscopic ellipsometry. Photoluminescence spectroscopy confirmed that the epitaxial GaN layers grown on a-sapphire at 600-700 C possess near band edge emission at $3.39 eV, close to bulk GaN. The GaN growth at 700 C without a buffer still produced films with better crystalline and optical properties, but their surface morphology and coverage were inferior to those of the films grown with LT buffer. The results show that the growth temperature strongly influences the structural and optical quality of LMBE grown epitaxial GaN thin films on a-plane sapphire, and a growth temperature of >600 C is necessary to achieve good quality GaN films.