An attempt has been made, probably for the first time, to understand the thermal evolution of non-spherical asteroids in the early solar system, with the short-lived nuclide, 26Al and 60Fe, as the internal radiogenic heat sources. Two numerical techniques, an explicit 3D-FDM (three-dimensional finite difference method) and a semi-implicit 3D-CNM (three-dimensional Crank-Nicholson method), have been developed on the basis of the central difference approximation to solve the heat conduction partial differential equation in cartesian coordinates for an assumed ellipsoid shaped asteroid. The second approach is based on fraction-step semi-implicit method (FSM) that turns out to be much faster in terms of computational time. The numerical techniques can be applied for any irregular shaped asteroids, TNOs (trans-Neptunian objects) or small satellites of outer planets. A comparison of the techniques has been made, for a spherical asteroid of radius 50 km, with the conventional explicit finite difference (FDM) and implicit Crank-Nicholson (CNM) methods based on spherical polar coordinates with temperature dependence on the radial coordinate alone. The newly developed techniques exhibit identical results, thereby, indicating a consistency in the distinct numerical approaches. Further, the results obtained from the techniques are also consistent at a level of up to ~96% when compared with the conventional numerical techniques during the several tens of million years of thermal evolution. The slight differences can be attributed to the nature of discretization (pixelization) of the ellipsoids into an assemblage of unit cubes that can result in a comparatively large surface area for more heat losses, and hence, results in comparatively rapid cooling. The thermal evolution of a wide-size range of asteroids having dimensions identical to (243) Ida, (951) Gaspra, (253) Mathilde, (5) Astraea, (6) Hebe and (3) Juno, was numerically simulated using the newly developed techniques to understand the heating and the cooling of non-spherical asteroids to understand thermal metamorphism. The cartesian coordinate corresponding to the shortest semimajor axis provides the fastest cooling to the ellipsoidal body. The accretion of the asteroids during the initial 2–3 Myr. could have provided diverse scenarios for thermal metamorphism.