What is the driving force for Heat Transfer?

Temperature gradient (Temperature difference) is the driving force for heat transfer.

According to second law of Thermodynamics heat will flow from high temperature region to the low temperature region under normal conditions. If we use external force, like heat engine, heat can be transported from low temperature region to high temperature region too.

In case of conduction, Fourier's Law gives that,

q α ΔT

So, we can say that heat flow is directly proportional to the driving force.