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Local thermal conductivity inside grains of high-quality polycrystalline diamond grown by chemical vapor deposition is measured at room temperature with micrometer spatial resolution. An effective conductivity is determined by choosing experimental conditions where the measured heat flow extends over adjacent grains. It is found that the effective conductivity may vary by a factor of 2, depending on the averaged volume and position on the sample. These variations are attributed to different grain structures present at the investigated locations. Local conductivity within a single grain varies by ±30% and a maximum value of 2350 W/mK is found. Local thermal conductivity data are related to the crystalline quality and impurity content determined by micro-Raman measurements.