The paper presents the results of computer simulations of unidentified transient heat transfer in the wall of a 35 mm cannon barrel for a single shot and for a sequence of seven shots with a subsequent firing break. The cannon barrel was made of 32CrMoV12-28 steel. For the phenomenon modelling, it was assumed that the material of the barrel wall is uniform and the barrel’s inner surface does not feature a protective coating of galvanic chrome or a nitrided casing. Calculations were performed for two input data variants: (i) for constant values of thermophysical parameters and (ii) for a temperature-dependent specific heat. The barrel with an overall length of 3150 mm was divided into 6 zones. On the inner surface of the barrel in each zone there were assumed various values of heat flux density expressed as rectangular functions in the range from 0 to 10 ms (with the start of ti of the function shifted in the subsequent zones). The calculation time for a single shot was assumed as equal to 100 ms. The calculations were performed with a finite element method in COSMOS/M software.