The thermal field of a shear flow near a plane wall, which was heated
with a harmonic source, was computed. For a linear profile of the flow
velocity, an exact expression of the spatial spectrum was obtained. T
he field itself was reconstructed from the spectrum using two methods:
analytical (for the asymptotics) and numerical (based on FFTs). The r
esults were compared with each other and with experimental data from t
he literature, and they were found to agree fairly well. Methods simil
ar to acoustic ray formalism were readily applied to the thermal wave
propagation in a flow. Under certain conditions, interference phenomen
a characteristics of regular wave processes were observed.