In this talk, I present my current project on temporal entanglement in quantum circuit models. In particular, we study dual-unitary Clifford circuits with  probabilistic measurements preserving spatial unitarity. We obtain exact results on characterizing the temporal entanglement barrier in the measurement-free regime. In the monitored regime, we numerically study the interplay between  measurement rate and bath size. We connect the initial diffusive growth of temporal entanglement with  bath size to a variant of  random walk model and provide an exact transfer-matrix approach for understanding how the system approaches the infinite-bath fixed point.