>>11064286The rate of heat transfer increases with a larger temperature difference between the object and its surroundings. This is because temperature is related to the average kinetic energy of the molecules.
If you throw two elastic balls at each other, and one is moving much faster than the other, the fast one will be moving a lot slower after the collision and the slow one will be moving a lot faster.
If they start out with about the same speed, with one a little slower than the other, then after the collision the fast one will only be moving a little slower and the slow one only a little faster.
This is a heavily simplistic picture of the average molecular behavior during heat flow.