This work examines the effect of black carbon (BC) radiative heating on cloud droplet formation. Changes in cloud droplet concentration and cloud albedo due to the presence of black carbon are computed for different cases of aerosol size distributions, meteorological conditions, BC mixing state, and aerosol composition. We examine the effect of three new mechanisms (that result from BC heating) that can affect cloud droplet number and lifetime. Two of these mechanisms act to increase cloud droplet number or lifetime: (1) the ability of BC to decrease the collection efficiency of giant cloud condensation nuclei (CCN) and (2) the delayed growth of low-Sc CCN that allow higher-Sc CCN to form droplets. These two mechanisms complement each other in terms of increasing cloud droplet number, since it is shown that the former is most efficient at strong updrafts and the latter is most efficient at low updraft velocities. A third mechanism identified, gas-phase heating (which is different from the so-called semi-direct effect), in our simulations acts to decrease LWC, and thus albedo; however, the droplet number concentration does not change significantly due to dynamic readjustments in cloud supersaturation. The simulations indicate that the mixing state of BC with the CCN population can have an important influence on the effect of BC heating on the droplet population. Although additional work is necessary to fully assess the effects of BC heating on cloud microphysics and climate, this work shows that these effects are more complex than currently thought.