Circadian clocks are characterized by three properties: they run in constant conditions with a period of ∼24 h, synchronize to the environmental cycles of light and temperature, and are temperature compensated, meaning they do not speed up with temperature. Central brain clocks regulate daily activity rhythms, whereas peripheral clocks are dispersed throughout the body of insects and vertebrates. Using a set of luciferase reporter genes, we show that Drosophila peripheral clocks are self-sustained but over-compensated, i.e., they slow down with increasing temperature. In contrast, central clock neurons in the fly brain, both in intact flies and in cultured brains, show accurate temperature compensation. Although this suggests that neural network properties contribute to temperature compensation, the circadian neuropeptide Pigment Dispersing Factor (PDF) is not required for temperature-compensated oscillations in brain clock neurons. Our findings reveal a fundamental difference between central and peripheral clocks, which likely also applies for vertebrate clocks.