Low power efficiency is one of the main problems of THz sources, colloquially known as the THz gap. In this work we present prototypes of THz devices based on whisker-crystals of a hightemperature superconductor Bi2Sr2CaCu2O8+d with a record high radiation power efficiency of 12% at a frequency of 4 THz. We employ various on- and off-chip detection techniques and, in particular, use the radiative cooling phenomenon for accurate evaluation of the emission power. We argue that such devices can be used for creation of tunable, monochromatic, continuous-wave, compact and power-efficient THz sources.