We illustrate the diffusion limit of wall heat transfer in fluid-solid suspensions by considering small colloidal particles dilute in a liquid at rest. Because such particles are agitated by Brownian motion, their self-diffusivity is modest, the fluid and solid phases share the same temperature, and mixture theory should predict the effective suspension conductivity. We show how thermophoresis creates suspension inhomogeneities, suggest ways to mitigate the latter with ultrasonic forcing, and examine consequences on heat transfer. To inform a debate on nanofluids heat transfer, we show that anomalous conductivity enhancements reported with hot-wire thermal conductimetry can be an experimental artifact of thermophoretic migration along the temperature gradient or timing in the observations. (C) 2008 Elsevier Ltd. All rights reserved.