SOME TBs are hotter and more difficult and are harder keepers than 'average", but it can be a very individual thing.
The "hotness" of some Thoroughbreds is directly related to how they are fed, conditioned, and kept. They are SUPPOSED to have alot of energy and drive to run while they are being raced, and they are fed and kept accordingly.
I bought my first TB gelding right off the track, uninjured and racing fit, and he was a handful for around 60 days, until his energy levels from the type of feed and conditioning he had been maintainted at/with came down to the levels of an "average" pasture kept trail riding/pleasure horse, and he adjusted to different surroundings and activities. When I say "handful" and "adjusted" its not like he was wild and got quiet--he was ALWAYS very well mannered from day one, but just had alot of "go" and was super-aware of things that first 60 days, (like different colored tar on the road, LOL)......after his let down/adjustment period, he was less concerned with changes and less energetic.
So, once he was adjusted to normal levels of grain, free pasture access, no more breezing/galloping workouts, and etc., he was no harder to deal with than any other horse. He still had "go" when I asked him for it, but was no longer driven to be ALWAYS going. He was not an easy keeper, but was not a particulaerly hard keeper either.
The main issue we had to work through was his right lead. He had been raced for several years and he ran "around the turn"-- meaning he was never asked to take the right lead, and when turning was always on the left lead... so that took some time and training.
I have owned and currently own TB mares-- some straight off the track, a couple already broodmares-- and I have not found them to be hard keepers as compared to other horses of similar size and age. Currently my three TB mares (2 established broodmares, one came off the track in October) are unblanketed outside 24/7 with a round bale and minimal grain and are doing great in the cold snowy MI winter.
None of the TBs I have owned were particularly expensive to buy (and a couple were free) but I got them knowing they would need re-training for whatever discipline I wanted to do with them, and in some cases they needed time off and/or re-habilitating from an injury.