An exact solution method is given for 3D heating over a rectangular region on a homogeneous plate. It has application to laser heating and cooling of electronic equipment. Based on Green's functions and new summation identities, significant improvements are given over the separation of variables method. Machine accuracy is possible, which can be used to both provide verification solutions and intrinsic verification. Basic building blocks for arbitrary space/time heat flux distributions and simplified expressions are provided. The method can also be used for many other boundary conditions using tabulated algebraic identities for summations. (c) 2011 Elsevier Ltd. All rights reserved.