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Any plasma in thermal equilibrium emits gravitational waves. In this talk, I show that, for wavelengths longer than the microscopic mean free path, the production is sourced by hydrodynamic fluctuations, while for wavelengths of the order of the inverse temperature it is sourced by scatterings. This latter mechanism is the leading one and I will show a consistent computation for a Standard Model plasma to leading order in coupling constants. I will show how the energy density of these thermally produced gravitational waves accumulates over the thermal history of the universe, contributes to the Neff parameter and constrains the highest temperature of the universe. The current theoretical uncertainty ∆Neff ≤ 0.001 corresponds to Tmax ≤ 2e17 GeV. I will show throughout the presentation how the methods and physical picture are related to analogous calculations for the QCD plasma.