Sugar is exceptionally soluble in water, and heating does increase its solubility. When you make caramel (or sugar syrup), you put sugar into a pan and a small amount of water, and heating brings it all into solution (you use a small amount of water because you have to boil the water off before you make the caramel).
Heating generally does increase solubilities, as you are supplying energy to break bonds in the solid. What sort of bonds exist in sugar?
For a graph that shows the increase in solubility of sucrose in water with temperature consult this linky.
Heating water does not increase the solubility of sugar, but it does increase the rate at which the sugar is dissolved.
When you heat a substance, the particles in the substance begin vibrating faster. In a liquid like water, this means the atoms have greater and greater kinetic energy until the atoms collide so forcefully with one another that the liquid starts to boil.
In this case:
The sugar dissolves much faster in hot water than it would in cold water because the atoms that make up the molecules of water are vibrating and colliding so forcefully against the sugar molecules, that the sugar is broken up in a really short period of time.
Kinetic Energy: in simple terms, the energy of motion