The present invention relates to a fluid line member for a modular fluid line system for passing therethrough a crystallizing, heat-sensitive working fluid, such as a synthetic polymer, a cellulose derivative or a solution consisting of cellulose, water and amine oxide. Such working fluids have a temperature-dependent viscosity and are subject to spontaneous decomposition phenomena under strong exothermic reaction. A temperature control of the working fluid is to be made possible by the fluid line member. This is achieved in that the fluid line member has a circular cross-section with a temperature control device instead of the core flow. According to the invention the temperature of the working fluid can thereby be controlled from the inside.