<p>The application of the thermoradiative effect of photodiodes, in which photons are emitted to a cold reservoir in the far-field, is a promising approach for renewable electricity generation. Here we derive the radiative limit of the output power density of an ideal thermoradiative diode (TRD) with an intermediate band (IB) using detailed balance calculations. The output power density of an ideal IB-TRD with a given bandgap energy and an optimal IB position increases with the device temperature, and simultaneously the optimal position of the IB shifts away from the mid-gap position due to the current matching constraint. Since the intrinsic carrier density needs to be significantly lower than the doping concentration to form a <i>p</i>–<i>n</i> junction at the operating temperature, IB-TRDs can be advantageous compared to single-junction TRDs consisting of narrow-bandgap semiconductors.</p>