The thermal and electrical conductivities of natural diamond and of diamond films were measured between room temperature and 1000 c. Natural type IIa diamond, which is the purest diamond, was found to have a room temperature thermal conductivity of 24-25 W/cm-K which drops to 4-5 w/cm-K at 1000 C. Two diamond films (2 mm thick) grown by microwave plasma CVD were found to have thermal conductivities that fell exactly on the curve for the natural type IIa diamond. The electrical resistivity of both insulating natural diamond and good-quality diamond films is around 1016(Omega) -cm, which has been shown to be the apparatus limited value. The resistivity decreases with increasing temperature to a value of 105 to 107(Omega) -cm at 1000 C. the best diamond films have electrical resistivities two orders of magnitude greater than that for natural diamond over the whole temperature range. These conductivity results, which are determined by the impurities and defects in the sample, thus indicate that the best diamond films currently being synthesized are as pure or purer than the best natural diamonds.