The enhancement of the atmospheric greenhouse effect due to the increase in the atmospheric greenhouse gases is often considered as responsible for global warming (known as greenhouse hypothesis of global warming). In this context, the temperature field of global troposphere and lower stratosphere over the period 12/1978-07/2018 is explored using the recent Version 6 of the UAH MSU/AMSU global satellite temperature dataset. Our analysis did not show a consistent warming with gradual increase from low to high latitudes in both hemispheres, as it should be from the global warming theory. In addition, in the lower stratosphere the temperature cooling over both poles is lower than that over tropics and extratropics. To study further the thermal field variability we investigated the long-range correlations throughout the global lower troposphere-lower stratosphere region. The results show that the temperature field displays power-law behaviour that becomes stronger by going from the lower troposphere to the tropopause.This power-law behaviour suggests that the fluctuations in global tropospheric temperature at short intervals are positively correlated with those at longer intervals in a power-law manner. The latter, however, does not apply to global temperature in the lower stratosphere. This suggests that the investigated intrinsic properties of the lower stratospheric temperature are not related to those of the troposphere, as is expected by the global warming theory.