A saturated solution means that at that specific temperature you cannot dissolve more of the solute into the solvent. In your case, if the solution is saturated then adding a crystal of the same salt, and stirring, would give you the best chance of determining of the solution is saturated or not. It is important not only to add the crystal but also stir because some salts dissolve slowly. If you just add the crystal and see it sink to the bottom that may indicate the solution is saturated or it may mean it takes time for the salt to dissolve.
Cooling the solution does not prove that the original solution was saturated. If it was saturated, cooling it may result in a supersaturated solution rather than crystallization of some of the solute. And if some salt does crystallize that would be expected even if the original solution was not saturated since most salts are less soluble at lower temperatures.
Heating would prove nothing and stirring vigorously would be pointless if there is no solute undissolved.