This paper presents the time-domain wideband spherical microphone array impulse response generator (TDW-SMIR generator), which is a time-domain wideband image source method (ISM) for generating the room impulse responses captured by an open spherical microphone array. To incorporate loudspeaker directivity, the TDW-SMIR generator considers a source that emits a sequence of spherical wave fronts whose amplitudes are related to the loudspeaker directional impulse responses measured in the far-field. The TDW-SMIR generator uses geometric models to derive the time-domain signals recorded by the spherical microphone array. Comparisons are made with frequency-domain single band ISMs. Simulation results prove the results of the TDW-SMIR generator are similar to those of frequency-domain single band ISMs.