European beech is one of the most common tree species in Europe and is generally suggested to play even more of a prominent role in forestry in the future. It seems to have the potential to partially replace Norway spruce, as it is less sensitive to expected warmer and drier conditions. It is, however, not well known in which regions these new plantings would be particularly favourable and if specific provenances may be better adapted to the new conditions than others. Therefore, we estimated the potential early height growth under climate conditions in 2040–2060 for 20 beech provenances across a region covering the Czech Republic and Slovakia. This Central European region is expected to experience considerably drier and warmer conditions in the future. For this exercise, we implemented a new neural network model developed from height growth information obtained from the open-access BeechCOSTe52 database. The simulations are driven by past and future climate data obtained from the WorldClim database of historical climate data and future climate projections. Simulations revealed that provenances originating from drier regions performed on average significantly better than those from regions with good water supply. Moreover, provenances originating from drier regions had a particularly large advantage in the relatively arid regions of Central Czechia and Southern Slovakia. We can also confirm that all provenances showed a high phenotypic plasticity of height growth across the whole investigated region.