The embedding of advanced simulation techniques in power cables enables improved thermal protection because of higher accuracy, adaptiveness and flexibility. In particular, they make possible (i) the accurate solution of differential equations describing the cables thermal dynamics and (ii) the adoption of the resulting solution in the accomplishment of dedicated protective functions. However, the use of model-based protective systems is exposed to the uncertainty affecting some model components (e.g. weather along the line route, thermophysical properties of the soil, cable parameters). When uncertainty can be described in terms of probability distribution, well-known techniques, such as Monte Carlo, are used to simulate the system behaviour. On the other hand, when the description of uncertainty in probabilistic terms is unfeasible or problematic, nonprobabilistic alternatives should be taken into consideration. This paper will discuss and compare three interval-based techniques as alternatives to probabilistic methods in the simulation of power cable dynamics. The experimental session will assess the interval-based approaches by simulating the thermal behaviour of medium voltage power cables.