Climate change has a major impact on the urban built environment, both with respect to the heating and cooling energy requirements, but also regarding the higher probability of confronting extreme events such as heatwaves. In parallel, the ongoing urbanization, the urban microclimate and the formation of the urban heat island effect, compounding the ongoing climate change, is also a considerable determinant of the building’s energy behavior and the outdoor thermal environment. To evaluate the magnitude of the complex phenomenon, the current research investigates the effect of climate change and urban heat island on heating and cooling energy needs of an urban building unit in Thessaloniki, Greece. The study comparatively evaluates different tools for the generation of future weather datasets, considering both statistical and dynamical downscaling methods, with the latter involving the use of a regional climate model. Based on the output of the regional climate model, another future weather dataset is created, considering not only the general climatic conditions, but also the microclimatic parameters of the examined case study area, under the future climate projections. The generated future weather datasets are then used as an input parameter in the dynamic energy performance simulations with EnergyPlus. For all examined weather datasets, the simulation results show a decrease of the heating energy use, an effect that is strongly counterbalanced by the rise of the cooling energy demand. The obtained simulation results also reveal the contribution of the urban warming of the ongoing climate change, demonstrating the need to perform a holistic analysis for the buildings’ energy needs under future climate conditions.