In the framework of the European fusion program for energy, EUROfusion funds the studies for the future fusion power demonstrator reactor DEMOnstration fusion reactor (DEMO). Commissariat à l'energie atomique et aux energies alternatives (CEA) is involved in the conceptual design of the superconducting conductors for the toroidal field (TF) and central solenoid (CS) magnets. The CEA design proposal corresponds to wind and react Nb3Sn pancake-wound coils using cable-in-conduit conductors cooled at about 4.5 K by forced flow of supercritical helium. This paper presents the latest thermal-hydraulic analyses performed on both TF and CS conductors. Two TF conductor designs have been analyzed, with nominal currents of 111 kA and 88 kA, respectively. The analyses were performed in normal (burn) and off-normal (quench) conditions. Burn simulations focused on the central and lateral pancakes with heat load corresponding to neutron heating. The central pancake is the most critical one regarding the magnetic field, while the lateral one receives a more important heat load from the casing. The influence of case cooling on temperature margin (ΔTma) was analyzed by means of a dedicated 2D Cast3M model. The ΔTma sensitivity to driving parameters such as conductor friction factor correlations was analyzed. The impact of interturn thermal coupling on temperature margin was also assessed. Quench studies were performed on the TF conductor, considering a quench initiated either on the innermost turn or at the middle of hydraulic length. Regarding the CS conductor, burn scenario was led on the latest design featuring a nominal current of 53.7 kA, focusing on the impact of ac losses and of dwell duration.