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Many energy-intensive industries, like the steel industry, plan to switch to renewable energy sources. Other industries, such as the cement industry, have to rely on carbon capture utilization and storage (CCUS) technologies to reduce their production processes' inevitable carbon dioxide (CO2) emissions. However, a new transport infrastructure needs to be established to connect the point of capture and the point of storage or utilization. Given a tree-shaped network transporting captured CO2 from multiple sources to a single sink, we investigate how to select optimal pipeline diameters from a discrete set of diameters. The general problem of optimizing arc capacities in potential-based fluid networks is already a challenging mixed-integer nonlinear optimization problem. The problem becomes even more complex when adding the highly sensitive nonlinear behavior of CO2 regarding temperature and pressure changes. We propose an iterative algorithm that splits the problem into two parts: a) the pipe-sizing problem under a fixed supply scenario and temperature distribution and b) the thermophysical modeling, including mixing effects, the Joule-Thomson effect, and the heat exchange with the surrounding environment. We show the effectiveness of our approach by applying our algorithm to a real-world network planning problem for a CO2 network in Germany.