The performance of gas-drilling (drilling oil and gas wells with air, nitrogen, or natural gas) is very unpredictable in many areas due to lack of proper design of drilling parameters because of limited understanding of gas–rock interaction which requires knowledge of heat transfer in the well system. Complete analysis of rock failure requires an accurate mathematical model to predict gas temperature at the bottom hole. The currently available mathematical models are unsuitable for use for the purpose because they do not consider the effects of formation fluid influx, Joule–Thomson cooling, and entrained drill cuttings. A new analytical solution for predicting gas temperature profiles inside the drill string and in the annulus was derived in this study for gas-drilling, considering all these three effects. Results of sensitivity analyses show that formation fluid influx can significantly increase the temperature profiles in both the drill string and the annulus. The Joule–Thomson cooling effect lowers the temperature in the annulus only in a short interval near the bottom hole. The drill cuttings entrained at the bottom hole can slightly increase the temperature profile in the annulus.