We propose a new abstract formalism for proba-bilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Au-tomata and Interval Markov Chains. In this context, we consider the consistency problem that amounts to deciding whether a given specification admits at least one implementation. In the context of Interval Probabilistic Timed Automata (with no timing parameters), we show that this problem is decidable and propose a constructive algorithm for its resolution. We show that the existence of parameter valuations ensuring consistency is undecidable in the general context, but still propose a semi-algorithm that resolves it whenever it terminates.