Migration models have evolved significantly during the last decade, most notably the so-called flow Fixed-Effects (FE) gravity models. Such models attempt to infer how human mobility may be driven by changing economy, geopolitics, and the environment among other things. They are also increasingly used for migration projections and forecasts. However, recent research shows that this class of models can neither explain, nor predict the temporal dynamics of human movement. This shortcoming is even more apparent in the context of forced migration, in which the processes and drivers tend to be heterogeneous and complex. In this article, we derived a Flow-Specific Temporal Gravity (FTG) model which, compared to the FE models, is theoretically similar (informed by the random utility framework), but empirically less restrictive. Using EUROSTAT data with climate, economic, and conflict indicators, we trained both models and compared their performances. The results suggest that the predictive power of these models is highly dependent on the length of training data. Specifically, as time-series migration data lengthens, FTG's predictions can be increasingly accurate, whereas the FE model becomes less predictive.