A dynamic one-dimensional model of the freezing of first-year sea ice with a snow cover is presented along with Matlab code. The model is based on historical models in the literature, and is primarily intended to design a computational tool that accurately simulates transient temperature changes within growing sea ice. This may complement temperature data at various depths and times in growing sea ice. The model is validated by comparing the simulated ice temperature profile and growth rate to thermistor temperature profiles measured in 1997 in McMurdo Sound, Antarctica. This comparison shows evidence of platelet ice growth. Despite this, an accuracy of ±0.4 o C is achieved throughout the entire ice temperature profile, when comparing simulated transient temperatures to data. The model is also used, with the inclusion of a 15mm thick snow layer, to correct a previously observed discrepancy between ice growth rates measured via banding structures in ice cores and the predictions of a steady state ice growth model.