In this thesis work we investigate the heat transfer through the electrical insulation of superconducting cables cooled by super fluid helium. The cable insulation constitutes the most severe barrier for heat extraction from the superconducting magnets of the CERN Large Hadron Collider (LHC). We performed an experimental analysis, a theoretical modeling and a fundamental research to characterize the present LHC insulation and to develop new ideas of thermally enhanced insulations. The outcome of these studies allowed to determine the thermal stability of the magnets for the LHC and its future upgrades. An innovative measurement technique was developed to experimentally analyze the heat transfer between the cables and the super fluid helium bath. It allowed to describe the LHC coil behavior using the real cable structure, an appropriate thermometry and controlling the applied pressure. We developed a new thermally enhanced insulation scheme based on an increased porosity to super uid helium. It aims at withstanding large heat loads, as needed for the High Luminosity LHC upgrade (HL-LHC). Experimental measurements of the new insulation showed a major improvement of heat extraction compared to the present state-of-the-art used in the LHC. We developed a theoretical heat transfer model quantitatively explaining the experimental results of the LHC and HL-LHC insulations. We identified the heat extraction mechanisms, mainly occurring through super fluid helium micro-channels. The average micro-channels dimensions were estimated to vary between few and dozens of µm, depending on the insulation scheme. In the model we considered the known laws describing the dynamic regimes of super fluid helium. However such laws were never demonstrated to be valid in the narrow channels typical of the cable insulation. We developed a new experimental device to investigate heat transport through microchannels. Micro-fabrication techniques were used to etch the channels down to a depth of 16 µm. We measured the classical laminar and turbulent regimes, thus demonstrating the validity of such heat transport laws independently from the channel geometrical shape and size down to these dimensions. To conclude, we used the obtained experimental and theoretical heat transfer results to determine the LHC and HL-LHC magnets stability. We estimated their quench margin and compared it to the beam induced heat deposit. The resulting difference allows a safe operation of the magnets.