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A transmission-line model of thermal noise in 1-D electromagnetic (EM) media is presented that can find both the magnetic and the electric contributions to the noise in arbitrary arrangements of isotropic material. The model is used to compute the noise performance of a negative-index metamaterial slab based on split-ring resonators and rods, when magnetic and electric noise are both significant. It is shown that the former rises rapidly in the range when negative index effects are obtained, due to the lossy magnetic resonance. Results for infinite and finite media are compared, and the effect of size is discussed. Results for the slab are also compared with the indirect prediction of standard EM theory, and shown to be identical.