The present paper addresses unidirectional, unsteady, heat conduction in regular solid bodies (large plane wall, long cylinder and sphere) with uniform initial temperature, thermophysical properties invariant with temperature and heat convection exchange with a neighboring fluid. A novel analytical/numerical procedure named the improved transversal method of lines (ITMOL) has been implemented to transform the one-dimensional, unsteady heat conduction equations along with the uniform initial temperature and the convection boundary conditions in rectangular, cylindrical and spherical coordinates into equivalent one-dimensional, "quasi-steady" heat conduction equations. The transformed "quasi-steady" heat conduction equations are nonlinear ordinary differential equations of second order with linear boundary conditions, which can be solved with any numerical method. The singular feature of this kind of "quasi-steady" heat conduction equations is that time appears embedded into them. In this work, the temperature profiles in the regular solid bodies are determined by a suitable combination of ITMOL and the finite-difference method. The center, surface and mean temperature profiles, as well as the total heat transfer in the large plane wall, long cylinder and sphere exhibit excellent quality for the full spectrum of mean convective coefficients (h) over bar (0 < <(h)over bar> < infinity) over the entire time domain 0 < t < infinity.