With the help of the elastic wave theory, in the perturbed approximation the density-of-states for vibrational modes and the specific heat axe studied for different hollow Si nanospheres, coupled with a semi-infinite substrate. We find that the modes of such coupled hollow spheres are significantly broadened and shifted toward low frequencies. The specific heat of the coupled hollow nanosphere is bigger than an isolated one due to the coupling interaction and quantum size effects. The predicted coupling and size enhancements on specific heat are probed in thermal experiments.