The thermal conductivity of graphene and ultrathin graphite (thickness from 1 to ∼20 layers) encased within silicon dioxide was measured using a heat spreader method. The thermal conductivity increases with the number of graphene layers, approaching the in-plane thermal conductivity of bulk graphite for the thickest samples, while showing suppression below 160 W/m-K at room temperature for single-layer graphene. These results show the strong effect of the encasing oxide in disrupting the thermal conductivity of adjacent graphene layers, an effect that penetrates a characteristic distance of approximately 2.5 nm (∼7 layers) into the core layers at room temperature.