Coupling endothermic and exothermic reactions in multifunctional reactors poses a challenge concerning the reactor temperature control. A reactor concept particularly suitable to combine high productivity and efficient thermal integration with moderate temperatures is presented. This is accomplished by operating an adiabatic fixed-bed reactor in an asymmetric reverse-flow mode with alternating production and regeneration cycles. The key feature of this reactor concept is a distributed heat supply during the regeneration cycle, enabling a rigid temperature control and efficient utilization of the heat capacity of the fixed bed. This issue is divided into two parts. The first part (this article) presents a short-cut method for analysis and for optimal reactor design as well as the experimental evidence of the existence of traveling endothermic reaction zones. The second part describes the experimental implementation of the concept in the prototype of a methane steam reformer for hydrogen production using controlled heat release by flameless combustion.