The problem of transient conduction from a heated cylinder to its surroundings is reviewed, and methods for calculating the transient temperature field are summarized. Three spatially uniform heat sources in the cylinder are studied: the impulse, step, and ramp sources. Both transform and finite-difference methods are examined, and results obtained with these methods are presented for a wide range of conductivities appropriate for most gases and liquids surrounding a conductive cylinder of varying length-to-diameter ratio.