We study the orientational ordering of 2-dimensional closely packed Janus particles by extensive Monte Carlo simulations. For smaller patch sizes, the system remains in the plastic crystal phase where the rotational degrees of freedom are disordered down to the lowest temperatures. There the liquid consists of dimers and trimers of the attractive patches. For large enough patch sizes, the system exhibits a thermodynamic transition into a phase with the stripe patterns of the patches breaking the three-fold rotational symmetry. Our results strongly suggest that the latter is a 2nd order phase transition whose universality is the same as that of the 3-state Potts model in 2-dimensions. Furthermore we analyzed the relaxation dynamics of the system performing quenching simulations on the stripe phase. We found growth of the domains of the stripes. The relaxation of key dynamical quantities follows universal scaling features in terms of the domain size.