Superconducting fault current limiters are unique devices that offer fast response to fault without need of an external triggering system. Therefore, they are interesting for industrial use, although their price is high. The principle of the resistive fault current limiter is based on the steep current-voltage characteristic of superconductors. When the current rises over the critical one, voltage on the superconductor rises steeply, and this mechanism blocks the increase of the current. Simultaneous appearance of voltage and current during this limiting period of operation generates a substantial amount of heat that is dissipated in the superconducting wire causing a rapid increase of its temperature. In this contribution, we further develop the idea that, during a limiting period, there is only a small difference between cooling by liquid nitrogen and adiabatic conditions. Using this approach, one can think about a current limiter free from a liquid coolant using a cryocooler. In this contribution, we discuss main differences in cooling conditions and test the idea on a short sample of the high-temperature superconductor REBCO conductor. We compare the behavior of identical samples cooled to the same temperature by liquid nitrogen and conduction cooled. If the realization can be achieved, the huge benefit would be an FCL with a tunable triggering current via its operating temperature.