We quantify the effect of clustering on the thermal conductivity of colloidal dispersions using silane-treated silica, a system engineered to exhibit reversible clustering under well-controlled conditions. We show that the thermal conductivity increases monotonically with cluster size and spans the entire range between the two limits of Maxwell's theory. The results, corroborated by numerical simulation, demonstrate that large increases of the thermal conductivity of colloidal dispersions are possible, yet fully within the predictions of classical theory.