Can a supersaturated solution get cooler during crystallization?
The system sodium sulfate (Na2SO4) / sodium sulfate decahydrate (Na2SO4 * 10 H2O) / Water might be an example.


Dissolving Na2SO4 in water is exothermic due to hydration.
Dissolving Na2SO4 * 10 H2O is endothermic (entropy effect).


Below 32.384°C Na2SO4 * 10 H2O crystallizes from aqueous solution, above 32.384°C water free Na2SO4.

The solubility of sodium sulphate shows the following unusual shape with a maximum at 32.384°C.



If you would now prepare a saturated solution of sodium sulphate at 32.384°C, and would then be able increase the temperature without precipitation of Na2SO4, you would get a supersaturated solution of sodium sulphate.

Putting a seed crystal of Na2SO4 into it should result in crystallization with the solution getting cooler during this process.

Note that the crystallization frees water molecules that were previously bonded through hydration. This will lead to an increase of entropy.