The potential impacts of climate change on wheat were assessed for Kulmsa area in central highlands of Ethiopia using the Agricultural Production Systems sIMulator (APSIM)—wheat model. The objectives were to (i) evaluate the performance of wheat under increased temperatures with or without changes in rainfall and carbon dioxide (CO2) levels and (ii) assess the response of different wheat cultivars to projected future climates under improved management practices (optimal nitrogen rate, planting date, and density) (IMPs). The model was first calibrated and used to identify ranges of IMPs. Then, the model was used to (i) conduct sensitivity analysis of wheat in response to assumed elevated temperature (T), with and without change in rainfall and CO2 level, and to (ii) evaluate average effect of future worst-case climate change scenarios as predicted by an ensemble of three global climate models (GCM) under highest Representative Concentration Pathways (RCP8.5) for three future time frames, NF (2010–2039), MC (2040–2069), and EC (2070–2099). The simulation was evaluated for three wheat cultivars (“early”, “medium”, and “late”) relative to their corresponding baseline values under the selected IMPs. The baseline climate was represented by the long-term (1980–2009) dataset and CO2 of 360 μmol/mol. Results showed that increased temperature above 4 °C alone had strong negative impacts on yields under the IMPs when CO2 staying constant at the baseline level. In contrast, climate change simulations with GCM projections under IMPs and elevated CO2 effect showed that wheat yield remained unchanged (− 0.4 to + 9%) for all three genotypes. This suggests that the IMPs and elevated CO2 were able to reduce the negative effect of elevated T on wheat yield as T stress did not go beyond optimal T range for wheat. Overall, climate change may not reduce wheat production in the climate of the location of study in the near future, midcentury, or end century.