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nRF51822 TEMP internal temperature sensor characteristic

I'm trying to use the internal temperature sensor of the nRF51 to know the die temperature. Its accuracy is specced as +/- 4 degC, even +/- 8 degC at the extremes. Does anyone know more properties of this uncertainty? Is it a fixed thing, that I can improve by calibrating an offset? Or is it noisy, something that I might filter out using multiple measurements?

Edit: See my own answer, the offset I measure is unusually large. Any thoughts where this might come from?