  Dynamical localization is the analog of Anderson localization in momentum
space, where the system's energy saturates and the single-particle
wave-functions are exponentially localized in momentum space. In the presence
of interactions, in the context of a periodically kicked Bose gas, it has been
argued that dynamical localization persists. Focusing on the Tonks (strongly
interacting) regime, we show that the many-body dynamically localized phase is
effectively thermal, a clear deviation from the breaking of ergodicity observed
in standard many-body localized systems. We relate the effective temperature to
the driving parameters, and thus quantitatively describe the loss of coherence
at large distances in this phase. Contrary to the non-interacting case, the
momentum distribution decays as a power-law at large momenta, characterized by
an effectively thermal Tan's contact. This is a rare example where driving and
many-body (dynamical) localization lead to an effectively ergodic state.
