Empirical field data describing daily and seasonal cycles in body temperature (Tb) of free-ranging Crocodylus porosus (32-1010 kg) can be predicted by a mathematical analysis. The analysis provides a mechanistic explanation for the decreased amplitude of daily cycles in Tb and the increase in 'average' Tb with increasing mass. Assessments of 'average' daily Tb were made by dividing the integral of the difference between measured values of Tb and minimum operative temperature by the period of integration, to yield a thermal index expressing relative 'warmth' of crocodiles. The average daily Tb of a 1010 kg crocodile was 3.7 degrees C warmer than that of a 42 kg individual in summer and 1.9 degreesC warmer than that of a 32 kg individual in winter. The success of this mathematical approach confirms that crocodiles are simple ectotherms and that there is unlikely to be a significant contribution to their thermal biology from physiological mechanisms. Behaviour, however, is very important even in large individuals. Crocodiles in the field typically move daily between land and water in cycles that vary seasonally. We predicted Tb for the reverse of these behavioural cycles, which more than doubled seasonal fluctuations in Tb compared with the observed fluctuations. We were also able to predict the Tb of very large, dinosaur-sized crocodiles in a similar climate to that at our study site. A 10 000 kg 'crocodile', for example, would be expected to have a Tb of 31 degreesC in winter, varying by less than 0.1 degrees C during a day when operative temperatures varied by nearly 20 degrees C, from 20 to 38 degrees C. The study confirms that, in low latitudes at least, large dinosaurs must have had an essentially high and stable value of Tb, without any need for endothermy. Also, access to shade or water must have been crucial for the survival of large dinosaurs at low latitudes. Furthermore, the finding of increasing 'average' Tb as ectotherms grow larger may have implications for the metabolic rates of very large reptiles, because the Q10 effect could counteract the downscaling of metabolic rate with mass, an effect that seems not to have been recognised previously
