A Floquet wave--based algorithm for solving an electric field time domain integral equation pertinent to the analysis of transient plane wave scattering from doubly periodic, discretely planar, perfect electrically conducting structures is presented. The proposed scheme accelerates the evaluation of fields generated by periodic constellations of band-limited transient currents via their expansion in time domain Floquet waves and use of blocked fast Fourier transforms. The validity and effectiveness of the resulting algorithm are demonstrated through a number of examples.