Which direction does heat travel from hot to cold or cold to hot
Heat energy travels from a system of higher temperature to a system of lower temperature until it reaches an equilibrium. In other words, heat moves from hot to cold until the two parts are at equal temperature.
Heat is the release of energy so hot to cold
Heat exchange is the correct term. Exchange implies that both parties give something to the other. The heat warms the cold and the cold chills the heat. I would guess there is no directional flow.