The advent of nanotechnology makes it possible to make constrictions of nanoscale size between contacting solids. For example devices or structures made of nanowires and nanoparticles can form a nano sized constriction. In these structures, the nanowires or nanoparticles are typically in contact with each other or another solid surface forming contact constrictions of the order of few nanometers. Understanding the thermal energy transport across the nano-constrictions is of critical importance in these applications. Our previous study derived the ballistic conductance across the constriction (Prasher, R.S., Nano Letters 5, 2155-2159 (2005)). In this paper, we further consider the wave effect of the phonons when crossing the constrictions. We show in the Rayleigh regime, where the dominant phonon wavelengths are much larger than the constriction sizes, the constriction conductance varies with temperature as T7

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