Abstract: For the stack of the standing-wave thermoacoustic refrigerator, the essential features of the time-averaged heat flux density distributions inside a thermally isolated thermoacoustic stack were theoretically studied. The analytical formulation of the accurate mean temperature difference ΔT_m was achieved. In comparison with experimental results and linearization results, the derived formula to calculate the mean temperature difference ΔT_m was proved to be correct. The position and characteristic parameters of stack for the standing-wave thermoacoustic refrigerator could be optimized with the use of analytical formulae obtained as follows. The optimal position of stack is x_S=f^-1(ΔT_m), optimal plate distance is 2y₀/δ_κ=3.3～3.4 and the plate thickness is 2l/δ_κ=0.7.