For superconducting accelerator magnets cooled by superfluid helium (T<2.2 K) the electrical insulation is the largest thermal barrier against cooling. These insulations are composed of wrapping creating micro-channels with dimensions on the order of 10 to 100 microns. Understanding the thermal phenomena at this level of confinement is necessary for the design of the cooling system of these magnets. The "bulk" thermal properties of the superfluid helium remain valid for dimensions of the order of hundred microns, but for higher confinement, the validity of the transport laws is still unproven. We propose to study experimentally the heat transfer in superfluid helium in tubes, alone or networked, with hydraulic diameters ranging from 50 microns to several microns. The studies will be undertaken in "pure" superfluid regime (Landau regime) and superfluid turbulence (Gorter-Mellink regime). These experimental measurements will be coupled to a direct numerical simulation using the two-fluid model of Landau (NS equations change.) An existing 2D code will have to be improved to simulate the two temperature regimes of superfluid helium.