Deep-learning based rainfall-runoff models, in particular long short-term memory networks (LSTM), have been shown to outperform traditional hydrological models at various tasks, both when used as purely data-driven models and when combined with process-based models in a hybrid setting. These tasks include predictions in ungauged basins (PUB) and regions (PUR), tasks which have traditionally been challenging for conceptual hydrological models. While the spatial generalizability of deep-learning based models has received a lot of attention, it is less clear how they generalize to unseen and warmer climate conditions, i.e. how suitable these models are for hydrological climate impact studies. To address this research gap, we assess the ability of three types of models including (1) fully data-driven (LSTMs), (2) conceptual (Hydrologiska Byråns Vattenbalansavdelning (HBV)), and (3) hybrid (LSTM-HBV) models to simulate streamflow under conditions warmer than those used to train the models by running a differential split sample test. That is, we trained the models using data from the historical period 1960–1990 and evaluated them on both data of this period as well as of the warmer period 2000–2023. We find that LSTMs, while being the most accurate during the 1960–1990 period, have inferior generalizability to the warm period compared to the hybrid and conceptual models. In addition, we show that when generalizing to the warm period, hybrid models have similar accuracy as LSTMs, independently of whether the entire streamflow distribution or extreme events such as floods and droughts are considered. However, for snow-dominated catchments, all models suffer from similar reductions in accuracy when simulating streamflow under unseen climate conditions and the LSTM is the most accurate model for all periods. A detailed look at the snowmelt simulations of the hybrid and conceptual model suggests that better process-representation might be needed to accurately capture the dynamics of snow-melt and -accumulation processes, which are highly sensitive to changes in temperature. We conclude that the hybrid models effectively combine the high accuracy of LSTMs when predicting in ungauged basins with the good generalizability under changes in climate of conceptual hydrological models. This makes them a suitable choice for hydrological climate change impact assessments, particularly in ungauged basins.