In polycrystalline CVD diamond of useful macroscopic dimensions, which may be considered for high heat flux applications, thermal conductivity parameters are largely determined by grain size resulting from growth morphology, defects and impurities in the material. Thermal conductivity has been measured in a number of state-of-the-art diamond samples, by the steady state technique, over the temperature range 6 to 400 K. The results are presented, and discussed in terms of microstructural differences between samples. At approximately 30 K, a departure from normal Debye type behavior is observed as a lowering of the predicted conductivity. At higher temperatures, this departure becomes less significant so that above approximately 350 K, where only Umklapp processes contribute to phonon scattering, the measured thermal conductivity is close to that predicted by the model and in good agreement with reference data for natural type IIa single crystal diamond. To account for the observed temperature dependence of conductivity, an additional phonon scattering term is used which may be described as Rayleigh scattering at low temperature by defects of 0.7 to 1.3 nm in size.