Stochastic Block Models (SBM) provide a statistical tool for modeling and clustering network data. In this paper, we propose an extension of this model for discrete-time dynamic networks that takes into account the variability in node degrees, allowing us to model a broader class of networks. We develop a probabilistic model that generates temporal graphs with a dynamic cluster structure and time-dependent degree corrections for each node. Thanks to these degree corrections, the nodes can have variable degrees, allowing for more complex cluster structures and for model interactions that decrease or increase over time. The proposed model is compared to an existing model without degree correction and its advantages in terms of global performances are highlighted. We propose an inference procedure based on Variational EM that provides the means to estimate time-dependent parameters while reducing the risk of local label-switchings.