Momentum-analyzed beams of 20 and $17.326 \frac{\mathrm{GeV}}{c}$ electrons with average currents of 4.23 and 4.55, and 9.48, 9.57, 14.4, and 15.66 \ensuremath{\mu}A, respectively, are predicted by special relativity to have average powers of 84.5 and 91, and 164.3, 165.8, 249.5, and 271.3 kW, respectively. This prediction is checked to 30% in a calorimetric experiment using the temperature rise in the cooling water of a high-energy beam dump at the Stanford Linear Accelerator Center. To our knowledge, this is the first macroscopic test specifically carried out to test this aspect of special relativity at these particle energies and power levels, although an earlier sequence of tests using copper as the heat absorber have been performed at this laboratory at lower power levels, and confirms the theory to higher accuracy.