Slow Horse = LESS Leg
Hot Horse = MORE Leg
Contrary to popular belief, adding more leg to a sluggish horse is NOT the way to get them to go faster. In fact, over time from ride to ride it will actually cause them to become even more deadened to the leg. A sluggish horse needs to be re-sensitized to the leg and by continually nagging them you are just teaching them that the leg is actually meaningless. So to get a sluggish horse to move, you need to not just kick them, but to give specific cues, know your other aids, and not be "the boy who cried wolf."
The hot horse, on the other hand, often needs more leg! And this is because they need to be de-sensitized to your leg. If you hold your leg off of them, when you do touch them that moment of contact is even MORE stimulating. Whereas if you keep your leg on you can ebb and flow the support and accustom them to the subtleties of your communication. Often a hot horse is also a nervous or excited horse - the support of your leg (the "hug") can be used to reassure the horse. And don't forget - STOP IS A SPEED TOO! More leg is needed to stop than go because honestly it takes MORE WORK!
At the end of the day, you need to RIDE BETWEEN YOUR LEGS!