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ALLEGRO is a general-purpose detector concept for an experiment at FCC-ee featuring a noble-liquid electromagnetic calorimeter (ECAL) as one of its central detectors. Noble-liquid calorimetry is a promising option for future particle physics experiments, applicable to both hadron and lepton colliders. This ECAL comprises 1536 multi-layer read-out electrodes, realised as Printed Circuit Boards, and an equal number of absorbers, all immersed in liquefied noble gas at cryogenic temperatures. The absorbers consist of metallic composites, with a lead core and a stainless-steel skin. Unlike the ATLAS experiment structure, the electrodes and absorbers in ALLEGRO are straight and inclined relative to the radial direction of the ECAL. The new design is also larger and heavier, requiring a rethinking of the assembly that supports the detection components. This work presents the thermomechanical finite element analysis of a third of the new ECAL, paying special attention to the displacements of the rings, the deflection of the absorbers, and the variation of the noble liquid gap, all at room temperature and under cryogenic conditions.