Circadian rhythms are the physiological oscillations with about 24 h periods that have period stability under various circumstances. While gene regulatory feedback loop has been proposed for the model of the origin of the circadian oscillation, my colleagues and I had proposed an alternative model. The cyanobacterial circadian clock can be reconstituted in vitro only by mixing the three clock proteins, KaiA, KaiB, and KaiC, with ATP. Namely, the ratio of phosphorylated KaiC oscillates every 24 h in the mixture. This simple biochemical reaction shows self-sustained oscillation like Belosov-Zhabotinsky reaction. Thus, KaiC phosphorylation rhythm can be core oscillator producing cyanobacterial circadian clock. In this paper, I will discuss entrainment of the "in vitro clock" by temperature cycles.