From the time dependent heat conduction and temperature distribution, an expression is derived for the time constant in a cylindrical fuel pin and cladding with axial coolant flow. The power production and the inlet temperature are functions of time. In the radial direction perfect mixing of the coolant is assumed. The average coolant temperature in a region is the average between inlet and outlet temperature assuming a linear rise in the axial direction. The set of partial differential equations can be solved by means of Laplace transform. The reciprocal of the roots of the characteristic equation for the temperature in the transform domain represents the time constants. The smallest root represents the dominant transient time constant. This dominant time constant is compared with a qualitative expression for the thermal relaxation time of a reactor after a power change given by Bethe. The numerical example used is a fuel pin in EBR-I Mark III in flowing NaK coolant at a core power generation of 1 Mw at various coolant flow conditions.