With the development of cryogenic technologies such as quantum computing, there is an increasing need for low-power cryogenic thermometers that minimize self-heating. Here, we report an anomalous temperature-independent logarithmic current slope, d(ln J)/dV, in heavily doped silicon p⁺n⁺ junctions with significant dopant interdiffusion and highlight the advantages of our device as a low-power, cryogenic thermometer. Electrical characterizations from 2 to 420 K reveal that, at low forward bias, d(ln J)/dV remains nearly constant, which yields a voltage-temperature responsivity that is nearly independent of bias current. The observed transport cannot be fully understood with conventional diffusion or direct band-to-band tunneling. Instead, the results suggest the contribution of trap-assisted tunneling. These results establish interdiffusion-broadened silicon p⁺n⁺ junctions as a route to low-power temperature sensors while providing insight into carrier transport in heavily doped semiconductor junctions.