Summary: We study the Hawking radiation emitted into the bulk by \((D + 1)\)-dimensional Schwarzschild black holes. It is well known that the black-hole spectrum departs from exact blackbody form due to the frequency dependence of the ‘greybody’ factors. For intermediate values of \(D (3 \leqslant D \lesssim 10)\), these frequency-dependent factors may significantly modify the spectrum of the emitted radiation. However, we point out that for \(D \gg 1\), the typical wavelengths in the black-hole spectrum are much shorter than the size of the black hole. In this regime, the greybody factors are well described by the geometric-optics approximation according to which they are almost frequency independent. Following this observation, we argue that for higher-dimensional black holes with \(D \gg 1\), the total power emitted into the bulk should be well approximated by the analytical formula for perfect blackbody radiation. We test the validity of this analytical prediction with numerical computations.