Consider a horse or cow. They generally eat grasses and other plants during the majority of their waking hours each day. The size of their mouth appears to be sufficient to enable sufficient food ingestion to maintain all bodily functions as well as body temperature, except is really cold climates.
Now consider a Diplodocus, a sauropod dinosaur that weighed around 11 tons or so, more than a dozen times the weight of a horse or cow. However, their skull and mouth are of a size that is comparable to that of a horse or cow. The question should occur: Could a warm-blooded Diplodocus have been able to eat enough food to provide all the necessary energy? It seems somewhat unlikely! Each of the cells in that much more massive Diplodocus body needs to use energy for normal bodily processes, such as using the Krebs' Cycle within each cell. In addition, the rather large surface area of the Diplodocus (around 30 times or more of that of a horse) means that the lost radiative heat energy from the skin would also be 30 or more times as high as for a horse of the same body temperature.
When estimates for the numbers are used, it seems unlikely that a Diplodocus, with its smallish head and mouth, could possibly ingest enough plant material to provide all the required energies. Examination of the teeth have convinced all experts that the sauropods (including Diplodocus) were all plant-eaters. Therefore, there seems to be a potential problem in thinking that they were warm-blooded.
UNLESS the environment was EXTREMELY warm! IF the air around a Diplodocus was consistently within a few degrees of its internal body temperature, the amount of radiative heat losses might have been small enough to permit a warm-blooded energy balance. If that were not the case, it seems that this might be a strong argument that they had to be cold-blooded!
No opinion either way is implied here. This is simply a thermodynamic energy balance analysis reasoning regarding energy-in and energy-out having to be essentially the same.
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C Johnson, Physicist, Physics Degree from Univ of Chicago