The world communicates to our senses of vision, hearing and touch in the language of waves, as the light, sound, and even heat essentially consist of microscopic vibrations of different media. The wave nature of light and sound has been extensively investigated over the past century and is now widely used in modern technology. But the wave nature of heat has been the subject of mostly theoretical studies, as its experimental demonstration, let alone practical use, remains challenging due to the extremely short wavelengths of these waves. Here we show a possibility to use the wave nature of heat for thermal conductivity tuning via spatial short-range order in phononic crystal nanostructures. Our experimental and theoretical results suggest that interference of thermal phonons occurs in strictly periodic nanostructures and slows the propagation of heat. This finding broadens the methodology of heat transfer engineering by expanding its territory to the wave nature of heat.