Without fabricating intermediate tunnel junctions or wafer bonding schemes for interconnecting the subcells, heterojunction bipolar transistor solar cells offer a promising new route in solar energy conversion. In this work, an improved theory for the three-terminal heterojunction bipolar transistor solar cell is presented with inclusion of non-ideal effects missing from the previous treatment, namely the non-radiative recombination and the thermal conduction losses that are inevitably present in realistic devices. Following detailed balance theory, the revised analytical formula for the cell conversion efficiency is derived, and the maximum efficiencies under different conditions are further calculated. Under the condition of 100 sun irradiance and 50% injection efficiency, a Gallium arsenide/Gallium antimonide-based solar cell operating at 465 K yields a maximum efficiency of 46.4%. Moreover, the effects of solar concentration, injection efficiency, and other key parameters on the cell performance are analyzed, and, consequently, optimal operating conditions and limiting factors on the conversion efficiency are determined. Simulation results show that such a solar cell operating with low injection efficiency under moderate concentration factor and low cell temperature can significantly boost its conversion performance. This work provides new physical insights for optimal designs, thus paving a route towards the development of low-cost high-performance solar cells.