Controlling thermal transport has become relevant in recent years. Traditionally, this control has been achieved by tuning the scattering of phonons by including various types of scattering centres in the material (nanoparticles, impurities, etc). Here we take another approach and demonstrate that one can also use coherent band structure effects to control phonon thermal conductance, with the help of periodically nanostructured phononic crystals. We perform the experiments at low temperatures below 1 K, which not only leads to negligible bulk phonon scattering, but also increases the wavelength of the dominant thermal phonons by more than two orders of magnitude compared to room temperature. Thus, phononic crystals with lattice constants ≥1 μm are shown to strongly reduce the thermal conduction. The observed effect is in quantitative agreement with the theoretical calculation presented, which accurately determined the ballistic thermal conductance in a phononic crystal device.