The safeguard of power equipments is assuming a major role in the deregulated electricity market, where a malfunctioning power system could be responsible for serious damages to a large number of system operators having access to the shared energy resource. In this context thermal monitoring of power cables represents a key issue in evaluating the risks associated with a given load management policy especially during emergency conditions. In particular this demands for reliable assessment models that should be able to predict the transient thermal behaviour when the load exceeds the nameplate value. In this connection the application of both simplified and detailed power cable thermal models is often complicated by the presence of uncertainties affecting the tolerances of the input data. The effect of these uncertainties could influence the final solution to a considerable extent. A comprehensive tolerance analysis is therefore required in order to incorporate the effect of data uncertainties into the thermal modelling process. To address this problem, in the paper the employment of interval mathematic is proposed. Several numerical results are presented and discussed in order to assess the effectiveness of the proposed methodology which offer a rough qualitative insight of the solution in a very short time, comparable to the time required for a deterministic numerical simulation.