Estimation of maximum diurnal LST is demanding for many studies. In this research, the time series of MODIS daily LST observations for both Terra and Aqua were analyzed from 2002 to 2016 in Iran. The relation of maximum observed LSTs in the study area was investigated with environmental variables of aspect, elevation, slope, latitude, Normalized Difference Vegetation Index (NDVI), and soil type. Two methods of correlation analysis, as linear approach, and Random Forest (RF) statistical approach, as a nonlinear approach, were used to analyze the effect and importance of mentioned variables on the occurrence of high LSTs. In correlation analysis, the results showed that NDVI and elevation had the highest correlations (− 0.66 and − 0.51) with maximum observed LSTs. In RF, the elevation showed higher importance than other variables. The bare and low lands in central part of Iran (deserts) had high maximum LSTs and the south part of Lut Desert, especially Rigzar, had the highest LSTs (80 °C extracted from Aqua platform) among all pixels in the study area. Unique aspects of environmental condition and sand dune soil type in this region could be the reason for recording highest LSTs. Finally, to estimate maximum diurnal LSTs, diurnal temperature model (DTC) was applied under clear-sky condition over Rigzar area. The estimated parameters of DTC model from MODIS were compared with INSAT3-D geostationary satellite.