An analytical method has been developed for the inverse problem in one- and two-dimensional heat conduction, when the temperatures are known at an appropriate number of the measuring points. On the basis of these known temperatures, a closed form solution is determined for the transient temperatures by using Laplace transform technique. This method first approximates the temperature data with a half polynomial power series of time. The resultant expression for an objective temperature and heat flux are explicitly obtained in the form of power series of time. Numerical results for some representative problems show that the surface temperature and heat flux can be predicted for not only one- but also two- dimensional heat conductions well by the present method.