The thermal conductivity, k, of nanoscale colloidal suspensions (also known as nanofluid), consisting of nanoparticles suspended in a base liquid, is much higher than the thermal conductivity of the base liquid at very small volume fractions of the nanoparticles. However, experimental results from various groups all across the world have shown various anomalies such as a peak in the enhancement of k with respect to nanoparticle size, an increase as well as a decrease in the ratio of k of these colloidal solutions with the k of the base fluid with increasing temperature, and a dependence of k on pH and time. In this paper, the aggregation kinetics of nanoscale colloidal solutions are combined with the physics of thermal transport to capture the effects of aggregation on k. Results show that the observed anomalies reported in experimental work can be well described by taking aggregation kinetics into account. Finally, we show that colloidal chemistry plays a significant role in deciding the k of colloidal nanosuspensions.