I have more than just that problem with the study. I have compiled a list of evidence for endothermy in non-avian dinosaurs:
Evidence #1: Air Sacs
Birds lungs obtain fresh air when exhaling and inhaling, because the air sacs pump and the lungs absorbs the oxygen. They need this for a high active lifestyle. We find signs of air sacs in some fossil dinosaurs, the most famous example being Aerostean, an allosaur, who has very bird like air sacs. In addition, ceratosaurs, coelurosaurs, and the early theropod Coelophysis have been found with evidence of air sacs. This suggests that they have a very high active lifestyle.
Evidence #2: Uncinate Processes
Uncinate Processes are spurs on the hind edges of birds ribs, giving the chest muscles more leverage when pumping the chest to improve oxygen supply. The size of these spurs are all depending on the bird's lifestyle and oxygen requirements. Non-avian maniraptoran dinosaurs have these spurs, and are similar to those in diving birds, indicating they need a high-capacity oxygen supply. These spurs have been found in Thescelosaurus, an ornithischian as well.
Evidence #3: Growth
The one thing that this new study used to prove mesothermy, and I think is not correct. When comparing the growth rate of dinosaurs to modern animals, you get numbers similar to this:
0.22 Kilograms - Slower than marsupials
1-20 kilograms - Similar to marsupials, slower than precocial birds
100-1000 kilograms - Faster than marsupials, similar to precocial birds, slower than placentals
1500-3500 kilograms - Similar to most placentals
25000 kilograms and higher - very fast similar to whales
This all depends on the size of the dinosaurs used to compare the animals. I see how you can tell metabolism of an animal, but it seems pretty difficult to see if it is endothermic or ectothermic.
Evidence #4: Posture and Gait
When it comes to what metabolism dinosaurs had, you can use their gait as an indication of it, because you get an idea of what lifestyle they had, and what requirements metabolically it would have. Reptiles (not counting snakes) have sprawled legs, are also ectothermic. You see the sprawled legs in the platypus as well, but it is endothermic. Dinosaurs have an upright, erect posture. This hints at a more active lifestyle.
Evidence #5: Feathers
This is the second biggest argument for endothermic dinosaurs. Some covering on the animals body would be big proof of endothermy. In the study, they ignored that, and even used Archaeopteryx. Yes, it had a slower metabolism than most birds, does not necessarily mean mesothermy. Feathers are also very useful, to not only warm an animal up, but to cool it down as well. They had control over their body temperature, and the only other animals alive today with feathers are avian dinosaurs, the birds. Are they mesothermic? No, they are endothermic.
Evidence #6: Polar Dinosaurs
This is in my opinion, the biggest argument for endothermy. An ectotherm in a cold environment, would be incredibly sluggish, and probably die easily. However, as evident in many birds and mammals, endotherms have no problems. With land based polar endotherms, you have a thick coating of fur of feathers keeping you warm. In the icy waters, you have blubber keeping you fat and warm. With a mesotherm, you would be not able to tolerate the cold as well as endotherms. An argument could be made that dinosaurs could have hibernated. However, animals like Leaellynasaura, and Troodon, show no signs of hibernation, or torpor. What the dinosaurs probably used was a lot of feathers, and blubber. I am aware leatherback sea turtles swim in the Arctic circle, but are they actually adapted for that cold of an environment?
Evidence #7: Diversity
While it may not seem like it, diversity is probably because of an endothermic lifestyle. Modern lizards, snakes, amphibians, and crocodilians are diverse, but not the level of non-avian dinosaurs. From therizinosaurs to pachycephalosaurs. Sauropods, hadrosaurs, Leaellynasaura (squee!) ceratopsians, tyrannosaurs, ect. Dinosaurs used to dominate the world. If they were endothermic, they would be able to quicker adapt to their environments, and expand and diversify into all shapes and sizes. It seems like one thing that makes dinosaurs famous also lends credence to endothermy.
In conclusion, I am glad we have a term for "lukewarm-blooded" or "not cold-blooded, not warm-blooded". Mesothermy. I like it. Mesothermy. Mesothermy. However, I disagree with the methods they used, and the ultimate conclusions. I will say this however. If any of the dinosaurs where to be endothermic, it would be, with no question, the theropods. If any of the dinosaurs were to be mesothermy, they would be the sauropods, early dinosaurs, and larger ornithischians.
I am no expert, and have done a lot of research, so don't get angry if I get something wrong. Let me know. Until next time!