It is critical in the metal continuous casting process to estimate the temperature evolution of the casted section along the machine from the meniscus (the point where liquid metal is poured) to the cutting machine, where the product is cut to commercial length. A convenient approximated model to achieve this goal with a feasible computational effort, particularly in the case of large sections, is the so-called travelling slice: the transversal section of casted product is subjected to different thermal boundary conditions (e.g., thermal flux, radiation, convection) that are found during the movement at constant speed from meniscus to the end of machine. In this work, the results obtained with the approximated travelling slice model are analyzed in the favorable case of an axisymmetric section. In this case, the reference model is 2D, whereas the travelling slice model degenerates in a simple 1D model. Three different casted shapes were investigated, rounds with diameters of 200 mm, 850 mm, and 1200 mm, spanning from traditional to only recently adopted product diameter sizes. To properly test the validity of the travelling slice model, other casting speeds were considered, even outside the industrial range. Results demonstrate the advantage of using the travelling slice, particularly the much lower computational cost without sacrificing precision, even at low casting speed and large dimensions.