The Grüneisen formula is one of the most important equations of state, in which the Grüneisen parameter plays a key role in the linkage of mechanical and thermal properties of materials. In the present work, for the first time, we investigate the dependence of the Grüneisen parameter on film-thickness and temperature via theoretical modeling and molecular dynamics (MD) simulations. The theoretical analysis gives two analytic expressions of a thickness- and temperature-dependent Grüneisen parameter, and the difference between the two analytic expressions lies in the quadratic or linear dependence on temperature. MD simulations are conducted on face-centered cubic (FCC) Ni, Cu, and Au (001) thin films and their bulk counterparts. The simulation results completely verify the theoretical results and determine the values of parameters involved in the theoretical modeling. The thickness- and temperature-dependent film heat capacity density is also investigated during the course of the Grüneisen parameter study.