What happens to the solute if you heat up a supersaturated solution? Since a supersaturated solution is already more than saturated with solute and unstable, my theory is that as you heat the supersaturated solution, the solubility limit will have been increased enough to allow all of the solute to dissolve. So technically, the solute does not precipitate out if you heat it enough.
If you sufficiently disturb a supersaturated solution, the solute will spontaneously come out solution. So you would need to heat it without sufficiently disturbing it.
The solubilities of some solutes decrease with temperature. So let's assume your solute's solubility increases with temperature (as is the case for most, but not all, solids dissolved in a liquid).
So if we allow for the above then, as you heat the solution, you will eventually reach at point at which it is no longer supersaturated.
Indeed, the reverse of this is how supersaturated solutions are typically prepared: A solution is prepared at a high temperature with a concentration of dissolved solid just below the saturation point (you don't want any undissolved solid left, since that will act as a nucleation site and thus prevent supersaturation). Then it is carefully cooled. So, by heating it sufficiently, you would simply be moving it back towards the starting point.
Finally, someone might argue that, if the solution is supersaturated near the boiling point, it might not be possible to heat it up sufficiently to get below the saturation concentration. I suppose that's possible in theory, but I don't know how you would prepare such a system, since it couldn't be created using the typical cooling process.