A theoretical and numerical analysis of a new conservative method based on finite difference techniques applied to the heat equations is presented. The proposed scheme produces better conditioned linear systems, approximations and more flexible discretization than standard finite differences techniques. On the other hand, it satisfies properties of continuous differential operators and discrete versions of integral identities, which guarantee its conservative properties. This last result and the convergence proof are shown in this study. In addition, illustrative numerical tests and a comparative study with one of the better approximations in finite differences are also included, providing evidence that the conservative method is a better choice to the numerical solution of boundary-layer like problems formulated in terms of the heat equation.