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We study the effect of thermal fluctuations in a vortex lattice driven in theperiodic pinning of a Josephson junction array. The phase diagram current ($I$)vs. temperature ($T$) is studied. Above the critical current $I_c(T)$ we find amoving vortex lattice (MVL) with anisotropic Bragg peaks. For large currents$I\gg I_c(T)$, there is a melting transition of the MVL at $T_M(I)$. Whenapplying a small transverse current to the MVL, there is no dissipation at low$T$. We find an onset of transverse vortex motion at a transverse depinningtemperature $T_{tr}(I)<T_M(I)$.Comment: 4 pages, 4 figures, Figure 2 changed, added new reference

Transverse Depinning and Melting of a Moving Vortex Lattice in Driven Periodic Josephson Junction Arrays