Benzoic acid is a weak acid that exhibits a very large discrepancy between its solubility in cold water verses hot water. The reason for this has to do with the molecule's large hydrocarbon body.
Like Dissolves Like
Solubility is dependent on the forces between molecules. These come in two camps: polar and non-polar. Polar molecules have electrically positive areas and electrically negative areas. The positive and negative areas move around to line up with each other, making the molecules mix together easily. Water is a good example. Non-polar molecules are more or less electrically even. When put together, they slide around each other without a problem, but they won't be attracted to polar molecules well.
Benzoic Acid: the Molecule
Benzoic acid has a large, non-polar benzene ring for the bulk of its body, attached to a smaller, polar acidic group. Therefore, it should be able to dissolve in either polar or non-polar solvents. While this is true, it doesn't particularly like doing either. It resists dissolving in water because the big non-polar body would much rather be around other non-polar benzene rings than polar water molecules, despite the acidic attachment.
The Effect of Heat
When you heat it all up, something else happens. The intermolecular attraction between the non-polar benzene rings drops off the hotter they get. Essentially, the molecules are bouncing around a lot more and can thus get separated more easily. With the molecules less attracted to each other, the water can get between them and dissolve the acidic component more easily.