Ballistic thermal transport properties by phonons in three dimensional (3D) periodic nanostructures is investigated. Results show that thermal transport properties in 3D periodic nanostructures can be efficiently tuned by modulating structural parameters of systems. When the incident frequency is below the first cutoff frequency, the quasi/formal-periodic oscillations of the transmission coefficient versus the periodic number/length can be observed. When the incident frequency is above the first cutoff frequency, however, these quasi/formal-periodic oscillations cannot be observed. As the periodic number is increased, the thermal conductance undergoes a prominent transition from the decrease to the constant. We also observe other intriguing physics properties such as stop-frequency gaps and quantum thermal conductance in 3D periodic nanostructures. Some similarities and differences between 2D and 3D periodic systems are identified.