Hydrodynamic propagators of forces are formulated and studied in the following cases: for uniform temperature, neglecting convection or using Oseen's linearization, with or without compressibility, and also for nonuniform temperature. Discussions and comparisons are given wherever possible. Such a propagator formalism is useful in cases of hydrodynamic interactions among solid bodies, as well as thermodynamic fluctuation forces. It is found that the velocity correlation functions describe a source with time‐dependent or ‐independent Oseen propagators. The correlation of pressure fluctuations, which exists even in the absence of dissipation, agrees with the result derived from the relaxation function of the mechanical fluctuation‐dissipation theorem, as well as with the thermodynamic equilibrium correlation. The correlation of temperature fluctuations describes a diffusion process of the variance&kgr;/&rgr;0cpwhencp = c&ngr;. In accordance with Curie's principle of nonequilibrium thermodynamics, it is found that the transverse vector field is not coupled to the scalar fields. Finally, a possible comparison with a wind tunnel experiment on temperature fluctuations is indicated.