The thermal conductivity of concentrated colloids in fluid, glass, and gel states was analyzed. SiO2 colloids at 10−31 vol % and Al2O3 colloids at 4.8 vol % in the fluid, the gel, and the glassy states were studied by dynamic light scattering, rheology, and transmission electron microscopy. Thermal conductivity of the three states was measured as a function of volume fraction. For the fluid and gel states the thermal conductivity increases almost linearly with concentration, reaching roughly 18% enhancement for silica at a volume fraction of 31 vol %. In contrast, in the glass state thermal conductivity strongly decreases with increasing volume fraction.