For the prevention of technical risks and the optimum design of an electrical distribution system, considerable efforts have been made to implement thermal models of wires, bundles, and electromechanical components in order to improve thermal analysis. Unfortunately, in most cases, important input parameters such as the position of a wire within a bundle or the profiles of the currents are unknown. This leads to the use of worst-case scenarios, frequently providing unrealistic results and uneconomic over-dimensioning.The proposed approach is based on the thermal simulation of a large number of randomly-generated bundle configurations for given profiles of currents. Thus one gets a temperature distribution, allowing a much more precise analysis compared to a simple worst-case calculation. By applying the same method to various current profiles, one gets temperature distributions for each wire as a function of a normalized total bundle current. The finding is that statistics allow a very good thermal assessment despite unknown bundle configurations and current profiles. The paper presents initial experimental data and simulation results followed by a discussion of future possibilities.