I actually thing that QH and most Stock type are considered warm blooded. Hot blooded horses stem from eastern origins, and include the Arabian, the Barb, and the thoroughbred (some people disagree and title the thoroughbred as a warm blood, others include many more breeds as hot blooded breeds.) I think that the TB is probably warmblooded but since a lot of family owned TBs are OTTBs they are more frisky and wild thus higher in on the temperament scale. Morgans would be warmblooded as a LOT of them are calm and collected while some can be hot an spooky. They are very versatile, used for driving, riding, showing, esp. Saddle seat, also Western, sometimes Hunt seat. They do just about everything but I think they are best in Saddle seat as mentioned even though mines Western. Thoroughbred include racing, steeplechasing, and as hunters in the show ring or in the field. Trakehner are very often used as jumpers, eventers and dressage horses, more so than Frisians. Missouri Fox Trotters are actually spectacular trail horses, more often than people think.
I don't think any one breed is the best a discipline, I think lots of different breeds could come out on top.