A neutrally buoyant float instrumented to measure 1-5 m shear and stratification was deployed for ten days in a near-inertial critical layer at the base of a warm-core ring. Vertical velocity and temperature data, from which large-scale (much greater than m) subinertial fluctuations have been removed, are used to estimate the vertical heat flux [w'T']. The resulting directly measured net heat flux is significantly nonzero and consistent with that inferred from microstructure measurements of turbulent dissipation rates epsilon and chi(T). The w, T cospectra tends to be negative at low encounter frequencies (f < omega(E) < 1.6N) and positive at higher encounter frequencies. The low frequency of the negative heat flux appears to be due to the intermittent co-occurrence of shear instability and wave-intensified stratification. The positive heat flux is associated with smaller scales (high Doppler frequencies) associated with secondary gravitational instability, fully three-dimensional turbulence, and restratification.