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We have developed compact and physics-based distributed numerical models for cryogenic bulk MOSFET operation down to 20 K to advance simulation and first-pass design of device and circuit operation at low temperatures. To achieve this, we measured and simulated temperature-dependent current-voltage characteristics of 0.16- and 0.18- bulk MOSFETs. Our measurements indicate that these MOSFETs supply approximately 40% more current in the saturation and linear regions of operation when they are cooled from room temperature to 20 K. The threshold voltage monotonically increases as the temperature is lowered, but it saturates below 40 K. The subthreshold slope decreases with the temperature lowering but at a rate that is less than theoretically predicted. The extrapolation of the subthreshold slope indicates a finite value at near absolute zero. We show that the measured behavior can be well corroborated with distributed numerical simulations using the drift-diffusion transport model. In addition, to obtain a compact model for use in low-temperature circuit design, SPICE-type compact models need to be modified to incorporate the subtle temperature effects that are not part of the standard models. To this end, we use the analog behavioral language Verilog-A and the BSIM3 model equation set to include additional temperature dependences into the standard compact models to accurately reproduce measured characteristics.