In the recent past, Andhra Pradesh (AP) has experienced increasing trends in surface air mean temperature (SAT at a height of 2 m) because of climate change. In this paper, we attempt to estimate the SAT using the GFDL-ESM2G (Geophysical Fluid Dynamics Laboratory Earth System Model version 2G), available from the Coupled Model Intercomparison Project Phase-5 (CMIP5). This model has a mismatch with the India Meteorological Department (IMD)’s observations during April and May, which are the most heat-prone months in the state. Hence, in addition to the SAT from the model, the present paper considers other parameters, such as mean sea level pressure, surface winds, surface relative humidity, and surface solar radiation downwards, that have influenced the SAT. Since all five meteorological parameters from the GFDL-ESM2G model influence the IMD’s SAT, an artificial neural network (ANN) technique has been used to predict the SAT using the above five meteorological parameters as predictors (input) and the IMD’s SAT as the predictand (output). The model was developed using 1981–2020 data with different time lags, and results were tested for 2021 and 2022 in addition to the random testing conducted for 1981–2020. The statistical parameters between the IMD observations and the ANN estimations using GFDL-ESM2G predictions as input confirm that the SAT can be estimated accurately as described in the analysis section. The analysis conducted for different regions of AP reveals that the diurnal variations of SAT in the IMD observations and the ANN predictions over three regions (North, Central, and South AP) and overall AP compare well, with root mean square error varying between 0.97 °C and 1.33 °C. Thus, the SAT predictions provided in the GFDL-ESM2G model simulations could be improved statistically by using the ANN technique over the AP region.