The dynamic model presented in the current paper estimates heat production and heat flow between growing and mature cattle (Bos indicus and Bos taurus) and the surrounding environment. Heat production was calculated using the NRC (2000) and heat flows between the animal and the environment were based largely on existing models and physical principles. Heat flows among the body core, the skin, the coat and the environment were calculated. Heat flows from and to the environment included solar radiation, long wave radiation, convection and evaporative heat loss. Physiological responses of cattle (sweating, panting and vasodilation) were modelled through mechanistic equations. The model required weather (radiation, temperature, wind and vapour pressure), animal (body-core weight and genotype-specific parameters) and dietary inputs (dry matter intake rates and diet composition) and estimated heat balance and the physiological responses of the animal to within-day weather variation. The current paper has focused on heat stress, although the model was designed to run under both hot and cold climatic conditions. The model developed in the current paper provides researchers and livestock producers with the ability to predict heat stress and to evaluate mitigating procedures.