I do think calmness and temperament, just as conformation, are inherited. Years ago I had an extremely calm Arabian mare. Bred to a very 'up' stallion, the offspring really took on the sire's behaviour. Bred to a very calm Arabian, the offspring was just like its parents - quiet and calm all its life.
My granddaughter, has a 30 year old Arabian gelding, who is wonderful and quiet around children and other animals, but is all fire on the trail. Few other horses can keep up with him. I hate to think what he was like as a youngster. I imagine his parents or at least one of them, was a spitfire.
I also had a calm Saddlebred and although he had been shown five gaited, away from the ring, he was just another ploddy fellow.
Certainly drafts tend to be calmer, but nice calm, ploddy horses can be found in any breed. Just have to seek them out.
Thinking about it, the worst and most difficult horse I ever owned, was a QH mare. Wonderful bloodlines and a beautiful girl, but a pretty dangerous one. I purchased her from some well known breeders, in the San Diego area. I still think she was probably doped up with something, the day I tried her out. She was wonderful then. I even sorted a few cattle with her. But the day she stepped out of the trailer, even the hauler had a difficult time with her. A completely different horse. She finally went to a trainer friend of mine, who got her under some bit of control, but she was definitely never a really safe ride for anyone. Even her new owner/trainer, said she was the most difficult QH he had ever come across.
Lesson learned. Show up when sellers are not necessarily expecting you. I should have known something was strange, since when I arrived at their place, she was saddled, bridled and standing almost asleep, at the rail. They didn't ride her, but brought out chairs to place by their arena, to all watch me ride. Strange all round. I didn't know better in those days. Some sellers, however well known, will do anything to sell a horse.