We study the thermal conductance of ballistic point contacts. These contacts are realized as few nanometer long pillars in so-called air-gap heterostructures (AGHs). The pillar length is orders of magnitude smaller than the mean free path of the phonons up to room temperature. Because of the small dimension and the low density of the pillars, the thermal conductance of the AGHs is several orders of magnitude reduced in comparison to bulk structures. The measurement results are in quantitative agreement with a simple model that is based on the Boltzmann transport equation.