In recent years, gasification gained attention again, both as an industrial application and as a research topic. This trend has led to the necessity to understand the process and optimize reactors for various materials and configurations. In this article, the thermal structure of a counter-current reactor is investigated to demonstrate that constraints on the temperature mainly determine the oxidation and the pyrolysis region. A non-dimensional set of equations is written and numerically solved using the method of lines (MOL) with spatial discretization based on a spectral algorithm. The results show that four thermal structures can be identified, two of which are the most common ones found in reactors of practical applications. Two stationary operation positions have been determined, one in the upper and one in the lower part of the reactor. Existence and stability conditions have been discussed based on non-dimensional parameters. The knowledge derived from this analysis was applied to two configurations, one typical of a biomass gasifier and one proposed for waste gasification.