In this work, we consider the estimation of temperature along the pipes of concentric heat exchanger tubes in which CO2 is the working fluid. The transport phenomenon is modeled using (2x2) linear hyperbolic partial differential equations, with one rightward equation for the hot flow and one leftward equation for the cold flow. Both flows exchange energy through the wall interface, which physically induces a coupling between the two dynamics. Our objective is to estimate the temperature distribution along the flows from measurements at the tubes boundaries only. In this framework, we propose an adaptive boundary observer that can estimate not only the full state of the system, but also unknown in-domain parameters. The design is based on transforming the error system via a finite-dimensional backstepping-like transformation into a desired filter-based system, for which standard backstepping observer techniques and adaptation laws can be used. The theoretical results are evaluated against the temperature measurements taken from a CO2 refrigeration apparatus built at CERN, Switzerland.