This paper focuses on adaptive output feedback control of transport-reaction processes described by semi-linear parabolic partial differential equations (PDEs) in the presence of unknown reaction parameters. Galerkin projection is applied to derive a low-dimensional reduced order model which employed as the basis for the adaptive controller design. The proposed control structure is a combination of a Lyapunov-based controller, an adaptation law and a static observer. The adaptation law is introduced to identify the unknown parameters while the static observer is employed to estimate the system modes required by the controller which cannot be measured directly from the process. The stability of the closed-loop system is shown using Lyapunov arguments. The effectiveness of the proposed low-dimensional adaptive output feedback control structure is illustrated on a tubular chemical reactor where the spatiotemporal dynamics of temperature and concentration are modeled by semi-linear parabolic PDEs. The control objective is considered to be thermal dynamics regulation in the presence of unknown heat of reaction.