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Here we investigate the use of single-junction InGaAs airbridge cells (ABCs) at elevated power densities. Such conditions are relevant to many thermophotovoltaic (TPV) applications, ranging from space to on-demand renewable electricity, and require effective management of heat and charge carriers. Experimental characterization of an InGaAs ABC with varying emitter and cell temperature is used to develop a predictive device model where carrier lifetimes and series resistances are the sole fitting parameters. The utility of this model is demonstrated through its use in identifying near-term opportunities for improving performance at elevated power densities, and for designing a thermal management strategy that maximizes overall power output. This model shows that an InGaAs ABC with material quality that leads to the longest reported carrier lifetimes can attain efficiencies exceeding 40% at 0.5 W/cm2, even when considering the power necessary to cool the cells.