An analytic analysis has been carried out to investigate the effects of temperature on the sound radiation from an unflanged circular duct by using a Wiener-Hopf technique. The wave equations were solved separately inside and outside the duct and the solutions were matched on the duct termination. Measured and computed results for uniform temperature in the duct are shown to be in close agreement. The results show that the radiation resistance is more affected than radiation reactance by the temperature difference between the gas and the ambient air. The radiation resistance is almost insensitive to, while radiation reactance decreases with, axial temperature gradients which increase the velocity potential in the duct as the wave propagates. At high frequency, the far field radiation pattern shows a second lobe as the temperature in the duct increases.