Prediction of extreme events under climate change is challenging but essential for risk management of natural disasters. Although earth system models (ESMs) are arguably our best tool to predict climate extremes, their high computational cost restricts the application to project only a few future scenarios. Emulators, or reduced-complexity models, serve as a complement to ESMs that achieve a fast prediction of the local response to various climate change scenarios. Here we propose a data-driven framework to emulate the full statistics of spatially resolved climate extremes. The variable of interest is the near-surface daily maximum temperature. The spatial patterns of temperature variations are assumed to be independent of time and extracted using Empirical Orthogonal Functions (EOFs). The time dependence is encoded through the coefficients of leading EOFs which are decomposed into long-term seasonal variations and daily fluctuations. The former are assumed to be functions of the global mean temperature, while the latter are modelled as Gaussian stochastic processes with temporal correlation conditioned on the season. The emulator is trained and tested using the simulation data in CMIP6. By generating multiple realizations, the emulator shows significant performance in predicting the temporal evolution of the probability distribution of local daily maximum temperature. Furthermore, the uncertainty of the emulated statistics is quantified to account for the internal variability. The emulation accuracy in testing scenarios remains consistent with the training datasets. The performance of the emulator suggests that the proposed framework can be generalized to other climate extremes and more complicated scenarios of climate change.