A solute can dissolve in solution until the open binding sites are fully saturated. This leads to over-saturation, or super saturated state. Not all molecules in a solution have exactly the same amount of potential or kinetic energy. Heat is energy, so therefore, by applying heat, the energy level is increased and more bonding sites are exposed. When heated, the molecules gain more kinetic energy and collide more frequently, adding to the exchange of kinetic energy for potential energy. Upon heating, the molecules must gain enough energy to reach a transition state, so this will depend on the amount of heat applied to gain the energy desired.
If you stir a soluble in a solution, the soluble will be dissolved until the solution's dissolving power reaches the maximum level. At one point, the level is exceeded, and the solution can not dissolve anymore soluble. But heat increases this power. If you make the temperature arise, the solubility increases too, and the solution can dissolve more solute, which means that more soluble can be dissolved into the solution then.