For NbTi magnets cooled by super¯uid helium (He II), the most severe heat barrier comes from the electrical insulation of the cables. Tests on electrical multi-layer insulations, made of Kapton â , dry ®ber and epoxy resin impregnated ®berglass tapes, indicate that heat transfer is in¯uenced by He II contained in the insulation. Electrical insulation can be considered as a composite material made of a solid matrix with a complicated helium channels network. For several insulations, this network is characterized by steadystate heat transfer experiment through an elementary insulation pattern. Measurements in Landau regime for low temperature dierence (10 À5 ±10 À3 K) and in Gorter±Mellink (GM) regime for higher temperature dierences permit to determine an equivalent He II channel cross-section 10 À6 m 2 ) with an equivalent channel thickness (25 lm). We use the assumptions that He II heat transfer through the channels network and conduction in the insulation are decoupled and that the channels length is determined from the insulation overlap. It is observed that He II heat transfer is competing with conduction in the insulation. Furthermore, the measurements reveal an anomaly of heat transfer in the vicinity of the k temperature which is associated to the phenomenon of k-point depression.