A symmetric superconducting quantum interference device (SQUID) with two Josephson junctions in the presence of thermal fluctuations is theoretically studied through two-dimensional Fokker-Planck equations. An analytical formula of the SQUID transfer function (or responsitivity) is derived by using the potential condition in the case of the steady state. It is found that the relationship between the optimum bias current Iopt and the thermal 0.80 ＜βopt ＜ 1.25, which is remarkably in agreement with the result of numerical simulation βopt ≈ 1.