This work presents an analytical method for computing the one-dimensional (1-D) acoustic field in milli-scale flows with a streamwise mean temperature gradient, where visco-thermal damping occurs due to wall interactions. Such flows are relevant to compact, high-performance heat exchangers, whose flow area between the tubes is characterised by a hydraulic diameter of the order of millimetres. We propose for the first time that an inviscid acoustic model incorporating mean flow and mean temperature effects can be combined with a wave number correction to account for visco-thermal losses. The proposed hybrid model requires the 1-D mean flow field as input, which was approximated from Reynolds-averaged Navier-Stokes simulations in this work, thereby accounting for mean shear effects. To evaluate the model predictions, comparisons were made against linearised Navier-Stokes equations simulations for inlet shear and Helmholtz numbers in the ranges 26 ≤ S hin ≤ 94 and 0.03 ≤ Hein ≤ 0.20 respectively. The model showed very good agreement across these ranges, particularly at higher Helmholtz numbers.