How do wind and ocean currents globally distribute heat energy?
It's called diffusion
Diffusion is the automatic process when particles move from a high concentration to a low concentration due to random thermal motion.
The warmer the particle is, the more it moves.
Wind is just molecules in the air that move to where it is a bit colder. That's why, if it's really cold in one place and warm in another, warm air will move to the cold place, however, the air may cool down before it reaches it.
It is the same with oceans. Warm water moves to the colder areas.
Diffusion makes sure that the heat gets distributed everywhere. Otherwise it would be much colder on and near the poles, and warmer near the equator.