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We present a numerical assessment of the thermal-hydraulic performance of the NbTi bus bars designed for the European DEMO. We consider the CS, TF and PF bus bars, as well as two alternative TF options for high-current operations. The main sources of static heat loads are identified and the corresponding thermal budget determined. In addition, the AC losses have been included in the simulations of the CS and PF bus bars, which present a pulsed operation, in contrast with the DC operation of the TF bus bars (and coils). By imposing appropriate pressure drops as boundary conditions, we compute the resulting He mass flow rates and the corresponding temperature margins along each bus bar. Thus, the most critical region of the bus bars in terms of cryogenic stability is identified, as well as the effect of AC losses on the temperature margin is quantified.