At the border between control and verification, parametric verification can be used to synthesize constraints on the parameters to ensure that a system verifies given specifications. In this paper we propose a new framework for the parametric verification of time Petri nets with stopwatches. We first introduce a parametric extension of time Petri nets with inhibitor arcs (ITPNs) with temporal parameters and we define a symbolic representation of the parametric state-space based on the classical state-class graph method. Then, we propose semi-algorithms for the parametric model-checking of a subset of parametric TCTL formulae on ITPNs. These results have been implemented in the tool Romeo and we illustrate them in a case-study based on a scheduling problem.