In this paper we present a novel emulator of a building simulator for the simulation-assisted design of high performance buildings. Our emulator is based on Gaussian-Process (GP) regression models. Such non-linear models are better suited than linear models as emulators because the simulator itself is a collection of non-linear models based on differential equations. We show that our proposed emulator is about 3 times more accurate than linear models in predicting the output of the simulator, achieving an average error of around 10-25 kWh/m2 for prediction of energy outputs that are in the range of 10-800 kWh/m2, compared to an error of around 50-100 kWh/m2 obtained by using linear models. Our emulators also heavily reduce the computational burden for building designers who rely on simulators. For example, the emulator can first be trained with observations from the simulator using a wide variety of building designs and weather data. This pre-trained model can then be used by building designers for exploration of new designs by predicting the performance of new buildings very quickly (in just a few milliseconds). We expect our approach to be particularly useful for Uncertainty Analysis (UA), Sensitivity Analysis (SA), robust design, and optimisation.