Dataset tabulates a) freezing front location vs time (1500 data points); b) penetration time sensitivities due to independent thermal conductivity and effective specific heat perturbations (1200 data points) ; and c) joint sensitivity of the combined thermal property perturbations (45 data points). All results tabulated against dimensionless input quantities: Biot number, cooling medium temperature, thermal conductivity, and latent heat. Front location vs time data generated by numerical 1D-slab freeezing simulations. Sensitivity data calculated using a novel approximate moving boundary mathematical model that considers convective cooling and temperature- depndent thermal properties.