Characterizing localized climate conditions is becoming important in many aspects of modern society. The Weather Research and Forecasting (WRF) models have been used to predict localized environmental variations. Further, the recently developed Urban Canopy Model (UCM), derived from energy balance equations, represents more detailed urban characteristics, when it is coupled with the WRF model. However, such physics-based numerical models can exhibit a spatially and temporally heterogeneous discrepancy pattern compared to actual climate conditions possibly due to inappropriate model specifications and/or incorrect choices of model parameters. This study devises a new method that post-calibrates geographically-and temporally-varying discrepancy in an integrative framework. Tested on urban temperature data collected in the central Texas region during heat wave events, our case study demonstrates that the proposed method substantially reduces prediction errors over the original WRF/UCM projection and other alternative approaches. Based on the results, we quantify the building energy consumption at spatially dispersed locations. Note to Practitioners: As electricity is a key component of modern society, the economy, and human well-being, the ability to assess the consumption of electricity is increasingly important. This assessment is challenging due to heterogeneous meteorological patterns. While the numerical weather prediction model, such as WRF/UCM, provides localized weather conditions, its output may not be accurate when its parameters and boundary conditions are not properly specified. In particular, we observe the prediction error from WRF/UCM is spatially-and temporally-varying due to the urban heat island effect during heat wave events. This study develops an integrative framework which provides a methodology to post-correct such heterogeneous prediction error. Our case study using data collected in the central Texas region suggests that the energy consumption at highly urbanized areas can be 0.4 kWh-0.5 kWh larger than its surrounding areas during the heat wave periods. The results demonstrate how the proposed approach can benefit a real application use case.