As long as the character does not become infected, his or her hit points will gradually recover if given proper rest and nutrition - Constructs have it even better than this since they will recover hit points at a fixed rate as detailed in their race description. Hard labour, combat, and heavy exertion will halve the recovery rate and double the chance of scarring. The rate of natural healing per day is equal to the character’s Constitution hit point bonus, or one point per day, whichever is greater.
Of course, a Construct's rate of natural healing is different than that of organic humanoids. If the Construct is not utterly destroyed, it will recover one Structural Point per day, whether or not it exerts itself.