Rhenium diselenide (ReSe2), which bears in-plane anisotropic optical and electrical properties, is of considerable interest for its excellent applications in novel devices, such as polarization-sensitive photodetectors and integrated polarization-controllers. However, great challenges to date in the controllable synthesis of high-quality ReSe2 have hindered its in-depth investigations and practical applications. Herein, we report a feasible synthesis of monolayer single-crystal ReSe2 flakes on the Au foil substrate by using a chemical vapor deposition route. Particularly, we focus on the temperature-dependent Raman spectroscopy investigations of monolayer ReSe2 grown on Au foils, which present concurrent red shifts of Eg-like and Ag-like modes with increasing measurement temperature from 77-290 K. Linear temperature dependences of both modes are revealed and explained from the anharmonic vibration of the ReSe2 lattice. More importantly, the strong interaction of ReSe2 with Au, with respect to that with SiO2/Si, is further confirmed by temperature-dependent Raman characterization. This work is thus proposed to shed light on the optical and thermal properties of such anisotropic two-dimensional three-atom-thick materials.