Inspirited by the wide range of applications of graphene and the similarity between boron and carbon, 2D boron sheets have gained extensive research interest. In this work, using first-principles combined with a nonequilibrium Green's function method, thermal conductance of fully hydrogenated borophene, named borophane, is studied. Interestingly and in contrast to widely perceived sense, at 300 K, it is found that the thermal conductance of borophane in the armchair direction is remarkably larger than that of graphene. More interesting, a dimensionality crossover is observed in phonon transmission where low-frequency phonons exhibit 2D characteristic, while high-frequency phonons behave like a 1D system, oriented along armchair direction, which results in the ultrahigh thermal conductance. An anomalous increase of thermal conductance with uniaxial tensile strain is observed, which is well explained by the unique puckered structure and chemical bonding in borophane. The excellent in-plane stiffness and flexibility together with the high thermal conductance suggest that borophane is promising for soft thermal channel. Moreover, this unique dimensionality crossover in phonon transmission offers a perfect platform for studying the effect of phonon population in mode space, which is of primary importance for thermal transport in low-dimensional systems.