In this article the distribution of temperature in both smooth and stepped functions is compared. The study uses a model of one dimensional N-cross-sections domain of a vase shaped medium, where approximation of the solution in the first case uses smooth functions, and in the second one, stepped functions. The temperature distribution is described by heat equation. Analysis of temperature distribution in both cases is based on finding eigenvalues and their corresponding eigen-functions which satisfy boundary conditions at given endpoints. Mathcad software was applied to determine the eigenvalues and their corresponding eigen-functions, together with the temperature distribution in the media of concern. The temperature distribution in both cases was found to be basically the same. The problem solution for each case is presented and an example of a one-dimensional vase shaped domain of length 4 units for each case is also given.