What is the term for an animal that maintains constant body temperature?

An endotherm, which is the useful term - warm-blooded is vague enough to be misleading. Endothermy means generating heat internally; homeothermy means holding a constant temperature; and the two are separable, which is why the old two-box classification keeps failing.

Plenty of animals sit between the boxes. Tuna and some sharks keep their muscles and eyes far above sea temperature using a heat-exchange arrangement in the blood vessels. Some large reptiles hold a steady temperature simply by being big, which is inertia rather than metabolism. Bees warm the hive collectively by shivering. Hibernating mammals abandon homeothermy for months and let their temperature fall to near ambient.

Endothermy is also extraordinarily expensive. A mammal or bird needs something like five to ten times the food of a reptile of the same size, essentially all of it burnt to hold temperature - which is why reptiles can survive on almost nothing and why the ecosystems that support large predators of each kind look so different. What is bought with it is being able to work at night, in cold, and at a constant rate, which turned out to be worth the price in most environments.