This work presents a summary of experimental data and theoretical models that characterize the temperature-dependent behavior of key carrier-transport parameters in silicon down to cryogenic temperatures. In extreme environment applications such as space-based electronics, accurate models of carrier recombination, carrier mobility, and incomplete ionization of dopants form a necessary foundation for the development of reliable high-performance devices and circuits. Not only do these models have a wide impact on the simulated DC and AC performance of devices, but they also play a critical role in predicting the behavior of important phenomena such as single event upset in digital logic circuits. With this motivation, an overview is given of SRH recombination theory, addressing in particular the dependence of recombination lifetime on temperature and injection level. Carrier lifetime measurement methods are reviewed, and experiments to study carrier lifetimes in the substrate of a commercial SiGe BiCMOS process are presented. The experimental data is analyzed and leveraged in order to develop calibrated TCAD-relevant models. Similarly, an overview of low-temperature resistivity in silicon is presented. Modeling of resistivity over temperature is discussed, addressing the prevailing theoretical models for both carrier mobility and incomplete ionization of dopants. Experimental measurements of the temperature dependence of resistivity in both p-type and n-type silicon are presented, and calibrated TCAD-relevant models for carrier mobility and incomplete ionization are developed. Finally, the ability to integrate these calibrated models within commercial TCAD software is demonstrated. In addition, applications for these accurate temperature-dependent models are discussed, and future directions are outlined for research into cryogenic modeling of fundamental physical parameters.