Exothermic reactions in solid powders are analyzed using the usual macroscopic modeling based on the heat transfer equation coupled to an Arrhenius type of dynamics. This problem have important applications in the synthesis of intermetallics and ceramic materials which occur when a high temperature reaction wave propagates throughout the system. Understanding the mechanism of such processes are thus crucial in mastering real laboratory experiments. We first analyze the model, both theoretically and numerically, for a set of representative parameters. We then use traditional data analyses procedures to estimate from the temperature profiles the same set of representative parameters. Comparison of imposed and estimated values of these parameters allows one to assess directly the limit of applicability and the accuracy of these data analysis approaches. A new strategy is finally derived, which gives a quite good estimate of the activation energy from the measurement of the local temperature profile.