In this study, the relationship between cosmic ray muons and the atmospheric temperature in the lower stratosphere has been investigated and established. Cosmic ray data from the KACST muon detector (Rc= 14.4 GV) and radiosonde measurements from Riyadh airport, for the period 2002-2012, have been used for this purpose. We have found that the temperature in the lower stratosphere is correlated with the cosmic ray muons detected at ground level. The results obtained are in agreement with previous studies. The technique was then used to predict temperature variations in the lower stratosphere. It was found that the temperature can be reproduced with a mean bias error of 0.5 o C and a root mean square error of 3 o C.