Global and regional observations of air temperature (AT) and specific atmospheric greenhouse gases (GHGs) such as methane (CH4) and carbon dioxide (CO2) are required for a variety of applications, including constraining global or regional estimates of their significant impacts on the climate system. The present study employs Atmospheric Infrared Sounder (AIRS) -Level3 monthly products for AT, CH4, and CO2, at two standard pressure levels (925 and 500 hPa) over Iraq during 2010–2016. Both CO2 and CH4 shows significant seasonal variation, with maximum (minimum) CO2 observed in June (October), while CH4 recorded three maximum peaks during April, August, and November, and a minimum in February. CH4 shows a negative correlation during winter (DJF), spring (MAM), summer (JJA), and autumn (SON) with correlation coefficients (R) −0.627, −0.734, −0.491, and −0.688, respectively. The P-value is below 0.05 (4.14 × 10−15, 2.13 × 10−22, 1.1 × 10−8, and 5.2 × 10−19) for the four seasons, indicating a negative linear relationship. CO2 shows a low negative correlation in DJF and SON, and a low positive correlation in MAM and JJA seasons, with R values equal to −0.315, −0.221, 0.059, and 0.079, for DJF, SON, MAM and JJA seasons, respectively. The P-value was greater than 0.05 (0.061, 0.728, 0.647, and 0.195) for the four seasons, respectively, indicating a nonlinear relationship with AT. The monthly averaged time-series for CH4 and CO2 shows an evident increase, with an annual average increase of 1.81% (4.75) ppbv/year and 3.31% (1.84) ppm/year, respectively. Analysis reveals that the major sink and sources for CH4 are the presence of hydroxyl (OH) radicals and vegetation, whereas the major sources for CO2 are anthropogenic emissions, burning fossil fuels, and land-use change. The satellite observations of AIRS can efficiently show the spatiotemporal variations of air temperature versus CH4 and CO2 for the study area.