Assumptions: Dragons are strict carnivores. Dragons are capable of flying, breathing fire, and otherwise sustaining life off some diet without the assistance of magic (however impossible that situation is).
Since they can breathe fire, would cooking their food be more efficient? Or would the cooking process destroy too many vital nutrients? Or would would it be more efficient if they cooked certain parts of their prey and ate the other parts raw? (If so what parts and why?)
There are a few reasons why it's useful to cook one's food:
Due to these factors, eating cooked food instead of raw would be a great advantage, so dragons with access to cooked food should be able to out-reproduce the competition and thus allow dragons to evolve into cooked-meat-eaters.
However, the question remains whether it would be worth the effort to cook the food. Humans don't need to expend constant energy to cook their food, they just need to rub two sticks together for a bit, then take turns tending the resulting fire. A constantly burning flame also provides many benefits to humans, such as illumination, heat, and protection from predators. If dragons develop the ability to build and maintain fires, then I think they could take advantage of some of these benefits, and also eventually learn to cook their food. If, on the other hand, dragons are not intelligent enough to build fires or don't need them (perhaps they are sufficiently self-heating and can see in the dark), then I don't think it would be worth the effort for a dragon to produce a constant stream of flame to cook its meat. Dragons that attempted to do so would be more likely to starve than others, so they would not win out in natural selection.
A dragon would probably not realize nutrient loss because it is so minimal, but they would certainly figure out that cooking meat will make it last longer. They may also enjoy the taste of the meat cooked. Cooking prey could also be a method of hunting. If the dragons were immensely intelligent or observant, they might also notice that cooking can kill harmful bacteria and that it would help aid digestion.
I'll go against the general trend, and say that no, dragons would, in general, not prefer cooked food.
Sure, a fire-breathing dragon would be pretty capable of inflicting burns on its prey, however inflicting burns sufficient to incapacitate or kill its prey is quite different to the process of exposing the deceased prey to sufficient heat over a sufficient time that it becomes effectively "cooked".
What is that difference? Energy. It takes a lot of energy to cook food, and while fiery breath is all very good for offence, defence and impressing the opposite sex, using it enough to cook prey would mean expending a lot of energy. Even if the energy stored in whatever combustible substance is being burned comes from an external source (e.g. Anne McCaffrey's Pernese dragons which eat phosphine-bearing 'firestone' in order to be able to produce a flame), gathering that energy would most likely not simply happen automatically. Since a dragon's flame is then a finite resource, any sensible dragon would reserve it for uses such as killing prey that it couldn't quite catch physically, self-defence, and impressing a prospective mate. This obviously precludes going on to cook that prey with it.
Even if a dragon's fire is magically generated at no metabolic cost to the dragon, it would still not make sense to use it to cook its food. Meat is best cooked at relatively low temperatures, like 200°C, not the 500°C+ temperatures that a dragon's traditionally 'very hot' flame might reach. Temperatures that high would result in the prey not being so much cooked as carbonised on the outside and raw on the inside. Applying the flame to prey for a longer period would eventually result in its insides being cooked, but there would be a very thick layer of carbonised flesh on top of that, flesh that would (unless magic was happening) have very little nutritional value left.
Dragons are also usually depicted as having long muzzles filled with carnivorous dentition, and while carnivores of the domesticated varieties don't have a problem with cooked meat as a rule, neither are they typically averse to eating a nice bloody chunk of flesh fresh from a carcass. I would not expect dragons to be particularly different in this respect.
So, a dragon might like playing with its food, setting its fur or clothing aflame and enjoying its subsequent antics before it expired or the dragon had to intervene again in order to kill it, but the end result would hardly be considered "cooked" food, being more "fatally burned" food which would still be essentially raw.
There might be occasions in which a dragon could trigger a wildfire or a structural fire which would effectively cook any prey trapped within, but this would probably be more an exception than a rule, and would result in a meal of somewhat less than usual nutritional value. Depending upon the dragon's level of intelligence, this would be of little significance to an unintelligent dragon, but for a partly or fully sentient dragon, it may have learned that if it triggers wildfires or structural fires, there will be a lot of "cooked" food afterwards, and it may have acquired an idiosyncratic taste for meals such as this.
TL,DR:
No, most dragons would be quite happy to eat their food raw, as the only means of "cooking" readily available to them is more likely to reduce the nutritional value of that food and increase the dragon's metabolic costs, and being of carnivorous descent, for the most part wouldn't share a herbivorous/omnivorous species' dietary preferences.
If they can control the fire and it doesn't take too much out of them to cook it, I would say yes. Most commonly, dragons are considered to be intelligent animals, at least on-par with humans. They hoard items and probably care how their food tastes, so I would assume they'd prefer it cooked if it tastes better.
It kills pathogens, it aids digestion and helps energy balance. It also tastes better to most if done correctly.
Cooking doesn't loose too much of it's nutrients. That link gives the maximum values of nutrient loss. Now it does mention that high temperature flames can create chemicals linked to cancer but cooking it at lower temperatures works well to prevent that. So as long as the dragons are careful, they should be fine. Give them a few generations.
I think dragons breathing fire because of they have a lot of heat inside. So they are indeffirent to cook their food with their breath cause it will be cooked inside the same. It pasteurizate the meat too.
Looking at the question with a bit of evolution in mind i think it could easily be justified that dragons will generally eat cooked meat.
Their ability to breathe fire is of course a marvellous weapon. Not only does being tunred into a torch often lead to losing the fight you are currently in, you also lose the fight if your surroundings are set on fire: being trapped in a burning patch of forest quickly turns most animals into food. And just setting fire to a forest might be a lot less energy consuming than actively finding your prey and hunting it: just wait for the local countryside to cool down a bit and leisurely go pick up the interesting bits of barbecue.
Obviously cooked meat has a lot less parasites, bacteria and so forth in it, so the dragon that consumes cooked meat has an advantage over a colleague that prefers raw meat since he does not die so often and spends less energy recovering from diarrhea (which often reduces the successful performing of mating rituals, too).
So after some genetic selecting, you will soon end up with all dragons prefering cooked meat.
Now as soon as intelligence enters the game, this effect will even speed up a lot, interestingly for the exact same reasons: the hunting style is efficient, tasty and healthy and it impresses the ladies. You can even get to know each other while the forest hunts and cooks dinner for you.
