High-temperature superconducting coated conductors (HTS-CCs) are good candidates for resistive superconducting fault current limiter (RSFCL) applications. However, the high current density they can carry and their low thermal diffusivity expose them to the risk of thermal instability. In order to find the best compromise between stability and cost, it is important to study the heat transfer between HTS-CCs and the liquid nitrogen (LN2) bath. This paper presents an experimental method to monitor in real-time the temperature of a quenched HTS-CC during a current pulse. The current and the associated voltage are measured, giving a precise knowledge of the amount of energy dissipated in the tape. These values are compared with an adiabatic numerical thermal model which takes into account heat capacity temperature dependence of the stabilizer and substrate. The result is a precise estimation of the heat transfer to the liquid nitrogen bath at each time step. Measurements were taken on a bare tape and have been repeated using increasing Kapton® insulation layers. The different heat exchange regimes can be clearly identified. This experimental method enables us to characterize the recooling process after a quench. Finally, suggestions are done to reduce the temperature increase of the tape, at a rated current and given limitation time, using different thermal insulation thicknesses.