I understand the definition of entropy regarding disorder or as some would say, the degree of energy dispersal and I understand how to calculate entropy (both change and absolute), however there is one aspect I would like some help with:

When we talk about Gibbs energy and the contribution of entropy towards determining whether a reaction is favourable (ie of the form ?G = ?H – T?S), how do you define the energy contribution that entropy makes? Similarly when we discuss the factors influencing dissolution of a compound, entropy can sometimes be a deciding factor. How is this entropic energy manifested?

It has units of J K-1mol-1 – ie the amount of energy required to raise the temperature of 1 mole of a substance by 1 Kelvin. Since entropy is essentially to do with the ratio of energy input to temperature increase, and temperature is a function of kinetic energy, are we saying that the energy contribution that entropy makes to a reaction equation is in the form of kinetic energy?