In this paper, we performed a four-dimensional numerical simulation to calculate wave propagation in a thermal fluctuating liquid metal in order to obtain detailed knowledge on a wave propagation in coolant material of a Sodium-cooled Fast reactor (SFR). The wave and the medium are described in three spatial and one temporal dimensions. We made use of a massive data set to describe the fluctuating situation of the medium. This data set was provided by Computational Fluid Dynamics (CFD) with a Large-Eddy Simulation (LES) model, which calculated the temperature field with a higher spatial resolution than Reynolds-Averaged Navier–Stokes turbulence models (RANS). This data set was furthermore obtained from other studies on a numerical and physical experiment called PLAJEST that created mixing jets of liquid metal in order to simulate the status of running SFRs. Because of the limitation of computational resources, previous acoustic studies applied to such a medium could only use the spatial-temporally averaged fluctuating heterogeneity of a medium calculated by RANS turbulence model. This limitation may overlook wave fluctuation because of the difference of the resolution between computational fluid dynamics and acoustic wave length. Our numerical effort allowed us to study the most realistic acoustic wave propagation in liquid metal than in any former studies. A new important result was obtained in this work as we demonstrated that ultrasonic measurements could follow thermal-hydraulic fluctuations in an opaque liquid with high sensitivity. This result was obtained through the definition of descriptors to analyse medium fluctuations along the wave path. We defined a very new measurement index, called hereafter Cumulated Temperature Fluctuation Intensity (CTFI), to correlate the variations in the thermal-hydraulic conditions to the wave variations. We demonstrated a good correlation between the second derivative of this index and the second derivative of several acoustic measurements, then we discussed the easiest measurements to be used in practice in an industrial setup.