Indirect fire hunting already exists, in multiple species.
Humans actually used fire to hunt, mainly in grasslands/ shrublands. Most well known in australia and north america. it takes two forms the native australians burn small patches of ground to kill small prey (especially burrowing animals) it has a side benefit of making the ground more attractive to other prey as the returning vegetation is more favorable. It helps that the sparseness of the scrubland means fires can't spread very far (55 acres max), it may even benefit the ecosystem by keeping hte vegetation in a patchy perpetually growing conditions instead of reaching maturity. There is some argument this was also used to hunt australia's megafauna to extinction, since it is rather easy to trap large animals with this methods. It is also used to clear land for native tuber farming.
In north america fire was used to drive herds into natural traps such as cliffs which would kill the animals for them, this is fairly wasteful but for something big like a dragon it may be less so especially if it is willing to scavenge the animals for a while afterwards.
surprisingly birds have also been known to hunt by spreading wildfires, so called firehawks (actually three different species of australian kite) use fire to hunt by picking up burning sticks and spreading fire to new places, this both kills prey directly and also flushes them out of cover making them much easier to hunt.
I know of no animal that uses fire directly to attack, but animals caught in wildfires may serve as a proxy, in grasslands they are mostly intact the fire is not long or incense enough to destroy anything, in forests however the intensity of a forest fire can destroy a carcass sometimes more or less completely. So just don't try to use fire hunting in a forest, this will be important for your characters safety anyway, forest fires are much less predictable. it is no coincidence that all these animals hunt in scrubland.
Fire is not going to damage anything you want.
Animals are not that flammable flesh does not burn readily or well, only high intensity forest fires or human created pyres can really destroy a carcass, and only because there is a LOT of external fuel to keep the fire going for a long time. Leather is commonly used as protection from fire precisely because it is very hard to ignite, even more so while still on flesh. So you don't have to worry about destroying the meat, fire mainly kills through asphyxiation or lung damage (scorching the lungs), occasionally skins may be charred but the underlying meat is rarely even touched, when it is it is more by cooking the tissue which you are going to do anyway. "Burns" are more often not really burned tissue but cooked tissue. The mechanics of DnD is not clear on how "fire" damage kills but I would assume it is similar to normal fire either cooking or lung damage.
I doubt firebolt will ruin an animal, if anything it may help, fire was used to clean hair off of skins, especially tough hair like hogs, hair burned but the rest of the carcasses is fairly fire resistant, which makes sense it IS mostly water. at worst burning may start the cooking process, again animals really are not that flammable.