This study utilizes an integral transform technique in order to solve the heat conduction equation in cylindrical coordinates. The major assumption is the high speed (i.e., large Peclet number) assumption. The boundary value problem is governed by the parabolic form of the heat equation representing the quasi-stationary state. The boundary conditions are a combination of Neumann and mixed type due to simultaneous heating and cooling on the surface of the cylinder. The surface temperature reaches a peak value over the heat source and gradually decreases to a nearly constant level over the cooling zone. Thermal penetration in the radial direction is shown to be only a few percent of the radius, leaving the bulk of the body at a uniform temperature. The width of the heat source and the total heat input are shown to be effective on the level of temperature whereas the input distribution is shown to be unimportant. The dimensionless numbers involved are the Biot and the Peclet numbers where the solution is governed by the ratio of the Biot number to the square root of the Peclet number.