The surface energy budget is important for understanding of energy and water cycle processes in the Tibetan Plateau (TP). In this study, the daily sensible (SH) and latent (LE) heat fluxes at the horizontal resolution of 1° are first estimated using the maximum entropy production (MEP) model (hereinafter SHMEP and LEMEP) in the entire TP during 2001–2022. The MEP model is built on physical and statistical principles to simulate surface heat fluxes. The surface net radiation, soil moisture (SM), and land surface temperature (LST) are the main driving variables for MEP model. To select the relatively accurate MEP input data, the merged surface net radiation (Rn–merged) under all-sky conditions are generated from CERES, ISCCP-FH, and ERA5 using the Bayesian Model Averaging scheme. Besides, the TP SM and LST from various data sources are evaluated using the in-situ observations at site scale. Based on the daily Rn–merged, ERA5 SM, CERES LST, and the MEP model, the daily SH and LE are estimated in the entire TP. The results show the daily SHMEP and LEMEP perform well at the validation sites, with the regional mean correlation coefficient (R) above 0.7, root-mean-square error (RMSE) of <19 W m−2, absolute value of bias and mean absolute error (MAE) below 11 W m−2. The monthly SHMEP has the regional mean R of 0.96 and RMSE of 6.30 W m−2 at all the measurement stations. For LEMEP, the regional mean R and RMSE values are 0.93 and 10.01 W m−2, respectively. The MEP simulation results are superior to the SH and LE in ERA5, ERA-Interim, MERRA-2, and JRA-55 reanalysis datasets and previous studies, especially for LE. Based on this new dataset, the spatial and temporal varying characteristics of SH and LE in the TP are analyzed. The annual mean SHMEP value are large in the western TP, the Qaidam Basin in the northern TP, and the Himalaya ranges, and small in the southeastern TP. The annual mean LEMEP has the maximum value in southeastern TP, and minimum value in western TP and the Qaidam Basin. The annual mean SHMEP and LEMEP over the entire TP are 34.79 W m−2 and 20.16 W m−2, with the significant declining trends of −0.17 W m−2 year−1 and − 0.052 W m−2 year−1 during the study period, respectively. The spatial distributions of the MEP surface heat fluxes and their trends are mainly influenced by the model inputs of Rn and SM in the TP.