Deterministic models describing heat transfer and microbial growth in the cold chain are widely studied. However, it is difficult to apply them in practice because of several variable parameters in the logistic supply chain (e.g., ambient temperature varying due to season and product residence time in refrigeration equipment), the product's characteristics (e.g., pH and water activity) and the microbial characteristics (e.g., initial microbial load and lag time). This variability can lead to different bacterial growth rates in food products and has to be considered to properly predict the consumer's exposure and identify the key parameters of the cold chain. This study proposes a new approach that combines deterministic (heat transfer) and stochastic (Monte Carlo) modeling to account for the variability in the logistic supply chain and the product's characteristics. The model generates a realistic time-temperature product history, contrary to existing modeling whose describe time-temperature profile Contrary to existing approaches that use directly a time-temperature profile, the proposed model predicts product temperature evolution from the thermostat setting and the ambient temperature. The developed methodology was applied to the cold chain of cooked ham including, the display cabinet, transport by the consumer and the domestic refrigerator, to predict the evolution of state variables, such as the temperature and the growth of Listeria monocytogenes. The impacts of the input factors were calculated and ranked. It was found that the product's time-temperature history and the initial contamination level are the main causes of consumers' exposure. Then, a refined analysis was applied, revealing the importance of consumer behaviors on Listeria monocytogenes exposure.