The paper solves the higher-dimensional inverse heat source problems of nonlinear convection-diffusion-reaction equations in 2D rectangles and 3D cuboids, of which the final time data and the Neumann boundary data on one-side are over-specified. Firstly, we derive a family of single-parameter space-time homogenization functions. Secondly, the temperature is obtained through the superposition of the homogenization functions and solving a linear system to satisfy the over-specified Neumann boundary condition. Thirdly, the unknown heat source is recovered by the back substitution of the numerical solution of temperature into the nonlinear governing equation. Numerical tests reveal that the novel method is very accurate to find the solution and to recover the unknown space-time dependent heat source function in the whole space-time domain, whose required extra data are very saving. (C) 2019 Elsevier Ltd. All rights reserved.