Enhanced conduction heat transfer via sinusoidal oscillatory flow through circular tubes connecting two fluid reservoirs maintained at different temperatures is examined. Using a multiscale expansion technique for the solution of the governing partial differential equation, the spatial and temporal temperature variation within the tubes is determined for low values of α2 Pr, where α is the Womersley number and Pr the fluid Prandtl number. From this result, a calculation of the effective thermal diffusivity is made and used to determine the enhanced conduction heat transfer from the high- to low-temperature reservoir. The enhanced heat transfer produced by the oscillations is shown to be proportional to the square of the oscillation amplitude and a function of the Prandtl number, the frequency, and the tube radius. Values of effective conductivity in liquid metals three orders of magnitude greater than the normal heat conductivity are shown to be readily obtainable under typical experimental conditions.