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Temporal networks allow representing connections between objects while incorporating the temporal dimension. While static network models can capture unchanging topological regularities, they often fail to model the effects associated with the causal generative process of the network that occurs in time. Hence, exploiting the temporal aspect of networks has been the focus of many recent studies. In this context, we propose a new framework for generative models of continuous-time temporal networks. We assume that the activation of the edges in a temporal network is driven by a specified temporal point process. This approach allows to directly model the waiting time between events while incorporating time-varying history-based features as covariates in the predictions. Coupled with a thinning algorithm designed for the simulation of point processes, SimHawNet enables simulation of the evolution of temporal networks in continuous time. Finally, we introduce a comprehensive evaluation framework to assess the performance of such an approach, in which we demonstrate that SimHawNet successfully simulates the evolution of networks with very different generative processes and achieves performance comparable to the state of the art, while being significantly faster.