Indian subcontinent witnessed a rise in surface air temperature (SAT) in recent decades, during the summer months of March, April and May. The monsoon core region (MCR) of India experiences a hot and humid climate, with temperatures typically highest in May and June before the onset of the monsoon. Global climate model (GCM) simulations of SAT are very much essential to understand the future climate of Indian MCR. Biases in GCMs simulations are due to insufficient knowledge of parameterizations and various assumptions that are made to simulate the complex interactions between land, ocean and atmosphere. The objective of this study is to correct the bias in the Coupled Model Intercomparison Project Phase 6 (CMIP6)–GCM simulations of SAT during March, April and May months over MCR for the historical period 1985–2014 and shared socio‐economic pathways (SSPs) SSP2‐4.5 and SSP5‐8.5 for the period 2015–2100. SAT dataset of fifth‐generation reanalysis (ERA5) of the European Centre for Medium‐Range Weather Forecasts (ECMWF) is used as reference dataset to perform bias correction for the historical period. Preliminary investigation of both SAT datasets has shown that there exists considerable warm bias (1.47°C) over the MCR. Bias correction is performed using a one‐dimensional convolutional neural network (CNN‐1D) and a convolutional long short‐term memory network (CNN‐LSTM) deep learning algorithm. The performance of these algorithms is evaluated with the statistical metrics such as root‐mean‐square error (RMSE), normalized root‐mean‐square error, Nash–Sutcliffe efficiency, mean absolute error, percent bias, correlation coefficient and dynamic time warping. RMSE and percent bias were decreased to 0.35°C and 0.8% with CNN‐LSTM algorithm. The CNN‐LSTM algorithm also preserves the year‐to‐year variability of SAT. Hence, CNN‐LSTM algorithm is found to be suitable for the bias correction of GCM simulations of SAT with encouraging results.