Why does temperature difference between 2 bodies affect rate of heat transfer?

[ms_kit]

Why does the different in temperature between 2 body determine the rate of heat transfer?
Why does the temperature gradient decrease as it reaches thermal equilibrium/fixed point of a substance?

Apart from using the equation Rate of heat transfer = kA (Difference in temperature) / d

How can we explain using particle nature of the substance?

 

[haruspex]

This is for conduction, yes?
At the molecular level, the temperature at some point in the body indicates the average energy per (motion state per) molecule. The individual molecules there will have various energies around that mean value. As they jiggle around, they bounce off neighbouring molecules. When two molecules interact so, there is an average tendency for their energies to become shared - i.e. the more energetic tends to lose some to the less energetic. The higher the temperature gradient, the more often the molecule from the hotter side will be more energetic than that from the cooler side, so the faster energy gets transferred.