This paper proposes a solution method for one-dimensional inverse heat conduction problems that require a relatively long time. A hybrid technique is applied to analyze laser surface heating and spray cooling on a hot surface. In the present study, the unknown temperature in half-range expansions form is assumed, and the shifting function method is used to obtain an analytic solution. The coefficients of the half-range expansions could be determined with the least-squares method in conjunction with the analytic solution and measured temperatures. Mathematical and experimental examples are given to illustrate the analyses. (C) 2016 Elsevier Ltd. All rights reserved.