Temperature distriburion in a hollow chlinder has been analyzed mathematically. Unsteady condition considered assumed a constant heat flux input from the inside. The results are compared with experimental results of surface temperature rise of a gun barrel during continuous firing. Their agreements are acceptable. Effects of various dimensionless parameters on the surface temperature rise are discussed. For small Biot numbers, the external survface temperature approaches more rapidly to the steady temperature. Temperature difference between internal and external surfaces becomes greater for small Biot number. Steady solution assumed that the gas temperature inside the cylinder varies periodically. Relative amplitude and phase angles between the gas temperature and the internal or external surface temperature are obtained. Phase angles become smaller for large radiancy of gas temperature variation, small external Biot number, or large internal biot number. Relative amplitudes become samller as radiancy of gas temperature variation and internal Biot number become smaller. or external Biot number becomes larger. The solution obtained in this paper can be applied to gun barrels, heat pipes used in heat excangers, and reciprocation engines.