We consider the parameter synthesis problem for multi-affine hybrid systems and properties specified using a hybrid extension of CTL (HCTL). The goal is to determine the sets of parameter valuations for which the given hybrid system satisfies the desired HCTL property. As our main contribution, we propose a shared-memory parallel algorithm which efficiently computes such parameter valuation sets. We combine a rectangular discretisation of the continuous dynamics with the discrete transitions of the hybrid system to obtain a single over-approximating semi-symbolic transition system. Such system can be then analysed using a fixed-point parameter synthesis algorithm to obtain all satisfying parametrisations. We evaluate the scalability of the method and demonstrate its applicability in a biological case study.