A conduction-cooled superconducting power transmission cable wherein a High-Temperature Superconducting (HTS) wire is surrounded by an inner layer of thermal insulator, one or more layers of high thermal conductivity material, such as copper, and an outer layer of thermal insulator with cryogenic coolant sources distributed along the power transmission cable and coupled to the copper layers or both the copper layers and the HTS wire. The cryogenic coolant sources can be reservoirs, a distribution system of coolant or stand alone refrigeration systems. He H2 or N2 liquid coolant can be used. A method for calculating the parameters to maintain the critical temperature of the HTS wire and a method for calculating the cool down time from ambient conditions are disclosed.