The coefficient of friction during braking is not constant. Determining its variability requires measurements in real conditions. This paper presents a methodology of conversion of the measured time profiles of the sliding velocity Veq, contact temperature T, and coefficient of friction f, into analytical formulation of two variables z = f(x,y). This was executed in the following steps: 1) creating a three-column table Veq, T, f from experimental measurements; 2) interpolation using Kriging; 3) creating a contour map of the coefficient of friction dependent on the sliding velocity and temperature, 4) import of a grey scale image of the friction map into the finite element (FE) software, and 5) definition of a function z = f(x,y). The studies were carried out for five composite organic friction materials and cast-iron brake disc of a railway vehicle. The developed five friction maps for each friction pair were based the data from the full-scale bench tests during braking from the initial vehicle velocity of 80 kmh−1, 120 kmh−1, 140 kmh−1, 160 kmh−1, 200 kmh−1 to a stop. In the second part of the study the initial-value problem for the equation of motion combined with the heat conduction problem were formulated and solved numerically using special functionalities of the FE software, e.g. Deformed Geometry, Mathematics. Changes in the vehicle velocity and time profiles of the coefficient of friction were determined from the solution of the coupled thermal problem. The computational FE model was verified by comparing the measured and calculated changes in the vehicle velocity, coefficient of friction and evolutions of the brake disc temperature during single braking. The maximum calculated temperature 1 mm under the contact surface of the brake disc, during braking from initial vehicle velocity of 80 kmh−1, was obtained for the base friction material and was equal to T1,3,5Num.= 72 °C. The corresponding experimental value was T1-6Exp.= 66.1 °C. When braking from 140 kmh−1, for the same material it was T1,3,5Num.= 129.7 °C and T1-6Exp.= 130.7 °C. The obtained differences in braking times calculated and measured did not exceed 1.7 %. The corresponding temperature differences of the disc at the stopping time were lower than 5.5 %.