Temperature represents an elementary environmental stimulus crucial for survival and fitness of organisms. Molecular membrane-based mechanisms for temperature sensing and behavioral response seem to be among the oldest principles of biological information processing. It is believed that some archaea -- early microbes prior to bacteria and eukaryotes -- developed thermoreceptors. In addition, they were able to maintain a circadian clock, a biochemical oscillatory system whose periodicity reflects a daily rhythm. Both features on their own, but especially their combination, gives raise for effective evolutionary advantage. Along with the notion of applied systems biology, we explore capabilities of resulting reaction models by exploitation of deterministic P modules and their dynamical coupling by means of simulation studies. Our findings indicate that a minimalistic circadian clock equipped with a chemical temperature sensor enables robust and practicable entrainment to an external daily temperature rhythm induced by the sun in contrast to a clock variant without thermoreceptor. Having a more adaptable circadian clock, archaea comprise better preconditions to populate larger oceanic regions from the equator towards the poles. From a modelling point of view, we incorporate the global quantity temperature and its effect on reaction velocity according to Arrhenius' equation into the framework of deterministic P modules.