Based on meshless natural neighbour petrovGalerkin method, a novel meshless method was developed to solve transient heat conduction problems with a source parameter. The essential boundary conditions cannot be enforced directly when the noninterpolative moving least squares (MLS) approximation is used. In order to overcome this difficulty, the natural neighbour interpolation was employed instead of the moving least squares approximation to construct trial functions. The local weak forms of the transient heat conduction problems were satisfied locally in a series of polygonal subdomains, which can be constructed easily with Delaunay tessellations. The traditional twopoint difference technique was selected for the time discretization scheme. A numerical example demonstrates the validity and effectiveness of the presented method.