High Temperature Superconductors (HTS) are promising candidates for high current Cable-In-Conduit Conductors (CICC) for large high-field magnets. In many cases, these CICCs are made from several HTS strands, which themselves consist of individual HTS tapes. Quench propagation in CICCs is currently under intensive investigation, and it can be predicted by modelling the entire cable structure. To model the heat transfer, along with material properties the thermal properties of contact interfaces between structural materials are highly needed. There are different kinds of thermal contacts in CICC: contacts between superconducting tapes stacked together, contacts between thin copper of stainless steel tapes, and between bulks of structural materials.