The kinetics of grain growth during thermally induced phase transitions between two block copolymer ordered phases have been determined by polarized optical microscopy (POM). Measurements were made on poly(styrene-b-isoprene) copolymers, f(PS) = 0.3-0.6, in solutions with dialkyl phthalates at polymer volume fractions of 0.5-0.7. When these solutions are cooled from a disordered state, they exhibit a transition from the transient metastable hexagonally perforated layer (HPL) phase to the gyroid (G) phase. The HPL to G transition typically occurs through classical nucleation, with radially symmetric grain growth, making it a model system for quantifying the growth front velocities of individual G grains. Temperature jump experiments monitored with POM were used to determine the effect of quench depth on the grain growth rates. Grain growth rates are compared quantitatively to the theoretical predictions of Goveas and Milner, with good agreement observed.