The thermodynamic properties of fully-hydrated lipids provide important information about the stability of membranes and the energetic interactions of lipid bilayers with membrane proteins (Nagle and Scott, Physics Today, 2:39, 1978). The lamellar/inverse hexagonal (L(alpha)-H(II)) phase transition of 1,2-dioleoyl-sn-glycero-3-phosphatidylethanolamine (DOPE) water mixtures is a first-order transition and, therefore, at constant pressure, must have a thermodynamically well-defined equilibrium transition temperature. The observed transition temperature is known to be dependent upon the rate at which the temperature is changed, which accounts for the many different values in the literature. X-ray diffraction was used to study the phase transition of fully-hydrated DOPE to determine the rate-independent transition temperature, T(LH). Samples were heated or cooled for a range of rates, 0.212 < r < 225 degrees C/hr, and the rate-dependent apparent phase transition temperatures, T(A)(r) were determined from the x-ray data. By use of a model-free extrapolation method, the transition temperature was found to be T(LH) = 3.33 +/- 0.16 degrees C. The hysteresis, /T(A)(r) - T(LH)/, was identical for heating and cooling rates, +/-r, and varied as /r/beta for beta approximately 1/4. This unexpected power-law relationship is consistent with a previous study (Tate et al., Biochemistry, 31:1081-1092, 1992) but differs markedly from the exponential behavior of activation barrier kinetics. The methods used in this study are general and provide a simple way to determine the true mesomorphic phase transition temperatures of other lipid and lyotropic systems.