One positive quality of a "hot" horse is that they never seem to get tired, but if you want something that you and your child can ride, I'd look for mellow! LOL

Of course, you will find horses in every breed that are "hot", its just generally Quater type horses are more quiet. Any how, maybe you can look at horses that were used in lessons for beginners and trial horses are good ones to look at, although you can find not so great trails horses! LOL

You are basicly going to have to pretty much search horse by horse and go out and look at them yourself and watch others ride them, etc. Just, don't judge a book by its cover. Also, when inguiring about a horse, tell them that you are a beginner with little expierence with horses and you need something for you and your child and the seller can more or less (hopefully if honest) tell you if your horse is suitable or not.