The conjecture that noise is always smallest in an equilibrium system is made quantitative for a transport problem by identifying noise with the noise temperature. In equilibrium the external fieldF=0, and the fluctuation-dissipation theorem gives = T, the temperature. In a strong fieldF the Boltzmann equation in the constant relaxation approximation is used to calculate the driftu(F, T) the diffusion constantD(F, T), and the noise temperature(F, T) for piecewise linear one-dimensional band structuresE(k). The validity of the noise inequality T has been shown for a large variety of band parameters and for all fields and temperatures.