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with the emergence of quantum technologies mastering thermal management is required, especially at the nanoscale. It is now accepted that thermal metamaterials (phononic diodes, themo-crystals) based on phonon manipulation are made possible especially at sub-Kelvin temperatures. In these extreme limits of low temperature and low dimension, phonon heat conduction enters into a quantum regime where the phonon exchange obeys the Landauer formalism. In this regime, phonon transport is governed by the value of the transmission coefficients between the ballistic conductor and the thermal reservoirs. Here, we report an ultra-sensitive thermal experiments made on a ballistic 1D phonon conductor using a new micro-platform suspended sensor. We achieved the measurement of thermal conductance with a resolution of $\Delta \mathrm{K}=\mathrm{K}$ of 1.5% and an unprecedented power sensitivity of few attoWatts around 100 mK. We show that the ballistic thermal transport is dominated by non-ideal transmission coefficients and not by the quantized thermal conductance of the nanowire itself. The measurements reveal scattering mechanisms dominated by phonon diffusion in the reservoirs. Since amorphous silicon nitride are used in that experiment we suspect that scattering of phonons on tunneling two Level systems (TLS) may be at the origin of the reduction of thermal transport. Complementary specific heat experiments are confirming that hypothesis of significant phonon-TLS scattering. The demonstration of the breakdown of the thermal conductance quantization is a major result for the phonon physics, showing that optimized thermal coupling to reservoirs from a 1D structure might be difficult to obtain. This limitation of heat transport in the quantum regime may have significant impacts on the design of modern thermal circuits and nanoelectronics (Josephson junction, quantum solid state devices). This high resolution experimental achievement gives new insight of heat transport in the quantum regime, a scientific goal that has remained uncertain till now.