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Résumé : We study thermal cosmological magnetic fluctuations in two complementary ways. First, we bound the equilibrium magnetic power spectrum in terms of two spectral moments. The proof uses the fluctuation--dissipation relation, spectral positivity, and the convexity and concavity of the thermal kernels. The bounds do not require a model for the spectral shape. They also apply to individual current contributions, using their own moments, and a known frequency threshold strengthens the upper bound. Second, we calculate a hadronic QCD contribution to cosmological magnetic fluctuations at leading electromagnetic order. We estimate the \(ρ\)-resonance contribution, which dominates the timelike hadronic contribution in our comparison. Examples from QCD, an electron--positron plasma and a cold collisional plasma test the bounds. The spectra describe fluctuations at the chosen cosmological epoch.