In the first part of this two-paper series, a new computational approach is presented for analyzing transient heat conduction problems in anisotropic nonhomogeneous media. The approach consists of a truly meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational Iteration (LVI) scheme for time discretization. In the present article, extensive numerical results are provided as validations, followed by a discussion on the recommended computational parameters. The FPM + LVIM approach shows its capability in solving 2 D and 3 D transient heat transfer problems in complex geometries with mixed boundary conditions, including preexisting cracks. Both functionally graded materials and composite materials are considered. It is shown that, with appropriate computational parameters, the FPM + LVIM approach is not only accurate, but also efficient, and has reliable stability under relatively large time intervals.