A test of the scaling of the extent of the thinnest vertical temperature gradients, in the near-bottom boundary layer on the Oregon shelf, shows that the Batchelor wave number determines the cutoff wave number in vertical temperature gradient spectra. In combination with previous results, in other words, this test shows that the smallest scale at which significant temperature variance due to turbulence exists at any given point in the ocean is determined by the Batchelor scale, (&ngr;D2/&egr;)1/4, &ngr; being the kinematic viscosity, D the thermal diffusivity, and the &egr; the kinetic energy dissipation per unit mass. Stress measurements in the viscous sublayer provide estimates of &egr;.