The transitory and stationary behavior of a quantum chaotic ratchet consisting of a biharmonic potential under the effect of different drivings in contact with a thermal environment is studied. For weak forcing and finite ℏ, we identify a strong dependence of the current on the structure of the chaotic region. Moreover, we have determined the robustness of the current against thermal fluctuations in the very weak coupling regime. In the case of strong forcing, the current is determined by the shape of a chaotic attractor. In both cases the temperature quickly stabilizes the ratchet, but in the latter it also destroys the asymmetry responsible for the current generation. Finally, applications to isomerization reactions are discussed.