Three 1,4-polybutadiene-1,2-polybutadiene diblock copolymers near the microphase separation transition (MST) have been examined theologically. The low-frequency linear dynamic shear moduli are shown to be strongly dependent on the phase state of these samples, which exhibit an upper critical temperature. Heating a microphase-separated (ordered) sample containing 38% 1,4-polybutadiene through the MST produces a discontinuity in both the elastic modulus and dynamic viscosity at a temperature Tm, corresponding to the first-order melt transition from the ordered to the disordered (homogeneous) state. Cooling from the disordered state produces no discontinuity in the moduli at Tm; instead, the polymer melt exhibits metastable behavior down to the stability limit in temperature, Ts< Tm. Below Ts, the viscoelastic response is characteristic of microphase-separated block copolymer, regardless of thermal history. These findings quantitatively verify the predicted phase behavior for diblock copolymers characterized by an upper critical temperature.