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Circadian rhythms are cycles in physiological processes that have a near-daily frequency. The wrist skin temperature has proven to be a good marker of circadian rhythmicity. In this paper we attempt to establish whether complexity changes in human circadian rhythms in ageing can be assessed through phase variability in individual wrist temperature records. To this end, we propose some phase complexity measures that are based on Lempel-Ziv complexity, Approximate Entropy, instantaneous phase, Hilbert transform and a complex continuous wavelet transform. A sample consisting of 53 healthy subjects has been studied. Our experimental results consistently show that a significant decrease in phase complexity happens when ageing.