[Note: Illustrations in these notes are from Morell, Virginia, 1996, A Cold Hard Look at Dinosaurs, Discover, vol.17, no.12 (December), pp.98-108. For more info read the article.]
Nasal turbinates are little, delicate spiral bones found in the nasal passages of animals. In warm blooded animals they are very important because they act to dehumidify the air you are exhaling. Why? Because otherwise you would suffer so much water loss that you would dehydrate very quickly. Let me explain.
Since we are "hot blooded" we breathe in about 10x more air per unit of time than a cold blooded animal. We need all that oxygen to keep the internal high metabollic engine going. However, the air in our lungs picks up moisture from our lungs and carries it as we exhale (think about the mist of water vapor we exhale when we can see our breathe on a cold winter's day). If we don't do something it will be lost. What we do is to pass this air through a labyrinth of spiral turbinates. As the air approaches our nostrils, it gradually becomes cooler (remember, if you are in a room with an ambient temperature of 70 degrees F, there is a 26.8 degree difference in temperature between your insides and your outsides!). As the air becomes cooler, the moisture condenses on the turbinates and is then returned to your body. Recycling keeps us moist!
Now the argument. All modern warm blooded animals (mammals, birds) have turbinates, so they must be necessary for a warm blooded animal. If dinos have turbinates then they were warm blooded. Guess what? They do not appear to have had them! Even though these small bones are rarely preserved as fossils, their presence is indicated by very large nasal passages (both wide abd voluminous - compare the illustrations of the dog (above) and the bird (below)).
On the other hand, modern cold bloods like crocs have tubular nasal passages which are narrow (look at the croc illustration below), and have no turbinates.
Dinos appear to have had narrow, tubular nasal passages (take a look at both the CT scan of Nanotyrannus (below), and the
illustration of dino nasasl passages (below), and compare them to the croc, the mammal, and the bird - the conclusions would appear to be clear. Dinos did not have turbinates, and therefore, were cold blooded.
Well, again, maybe. The possibility always exists that the dinos had developed some other way to prevent water loss, or maybe they had small turbinates (an unlikely possibility).
The jury is still out.