There is a potentially detectable background of stochastic gravitational waves produced by thermal sources in the Universe. In this work, we provide the first computation of the gravitational-wave spectrum emitted by a thermal plasma in a strongly-coupled theory: strongly-coupled $\mathcal N$=4 Super Yang Mills. Given the non-applicability of perturbative methods in strong coupling computations, we resort to gauge/string duality to obtain the shape of the spectrum. We later compare it with the analogue spectrum derived from the perturbative analysis in weakly-coupled Super Yang Mills. The convolution of both spectra with the expansion of the Universe provides the stochastic background of thermal gravitational waves that is present in the Universe. This work aims to mark the beginning in the study of the thermal emission from strongly-coupled cosmological sources, what could be relevant in the research of dark matter and other cosmological implications.