Temperature does affect the saturation point; at higher temperatures more solute can be dissolved in a solution than would be possible at lower temperatures. A good example of this is the fact that warmer air can hold more moisture than cooler air.
The saturation point is the amount of solute that can be added before no more can be dissolved into the solution. If the temperature is lowered after saturation is reached, supersaturation occurs. This is where a solution contains more dissolved solute than would be possible at the current temperature. Sweetened iced tea is made by heating up tea and dissolving sugar into the hot solution then cooling it down to a supersaturated solution.