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Aims: Spectral and temporal analysis of the NuSTAR observation Galactic Be-XRB Swift J1845.7-0037. during its recent outburst. Methods: For the spectral analysis we use both phenomenological and physics-based models. We employ an often used empirical model to identify the main characteristics of the spectral shape in relation to nominal spectral characteristics of X-ray pulsars. Additionally, we used the latest version of Bulk \& Thermal comptonization model (BW), to assess the validity of the spectral components required by the empirical model and to investigate the origin of the hard X-ray emission. We also analyzed the source light-curve, studying the pulse shape at different energy ranges and tracking the spectral evolution with pulse phase by using the model independent hardness ratio (HR). Results: We find that while both the empirical and physical (BW) spectral models can produce good spectral fits, the BW model returns physically plausible best-fit values for the source parameters and does not require any additional spectral components to the non-thermal, accretion column emission. The BW model also yielded an estimation of the neutron star magnetic field placing it in the 10^12G range. Conclusions: Our results, show that the spectral and temporal characteristics of the source emission are consistent with the scattering processes expected for radiation dominated shocks within the accretion column of highly magnetized accreting neutron stars. We further indicate that physically-derived spectral models such as BW, can be used to tentatively infer fundamental source parameters, in the absence of more direct observational signatures.