It has been increasingly reported that aerobic soil respiration activity (CO2 production and O2 consumption) is measurable in frozen cold-climate soils. This study modifies the Generalized Respiration (GRESP) model, a function of soil temperature (T) and unfrozen water content (M), to cover the frozen, partially frozen and unfrozen phases of successfully bioremediated, petroleum hydrocarbon-contaminated, sandy sub-Arctic soils. The Michaelis-Menten equation was modified to express the observable change in unfrozen water content near 0?°C, which is related to soil respiration activity during soil phase changes and at temperatures below the effective endpoint of detectable unfrozen water at -2?°C. The modified Michaelis-Menten equation was further combined with a Q10 temperature term, and was then incorporated into the GRESP equation to produce a new URESP model for the engineered soil bioremediation system at sub-zero temperatures. The URESP model was applied to published input data measured from the biostimulated site soils of a pilot-scale soil tank experiment conducted between -5 and 15?°C. The model fit well with the experimental data for CO2 production (R2?=?0.96) and O2 consumption (R2?=?0.92). A numerical soil thermal model (TEMP/W model) of the thawing biotreated soils in the tank was also used in this study to produce valid alternative (predictive) input T and M data for the URESP model. The URESP-derived respiration quotients (RQ; 0.695 to 0.698), or the ratios of CO2 production to O2 consumption, aligned with the experimental RQ values from the soil tank experiment (0.69) and fell within the theoretical RQ range for aerobic hydrocarbon degradation (0.63-0.80). The URESP model combined with the TEMP/W simulation approximated changes in soil respiration during thawing and characterized the computed soil respiration outputs as related to hydrocarbon utilization, based on their RQ values.