What characteristics must a solvent being used for recrystallization of vanillin should have to obtain the best results? One characteristics I could think of is it has to be cold.

The solid must have high solubility at high temperature and much lower solubility at low temperature in the solvent or mixture of solvents chosen.

The solid is dissolved at high temperature in the least volume of solvent, then cooled off. Unless the solution becomes supersaturated, the "excess" solute is crystallized and can be separated.
Vanillin can be dissolved in boiling water and re-crystalized by cooling in an ice bath.

To obtain the best results for recrystallization of vanillin, the solvent should possess several characteristics. Here's an explanation of each characteristic:

1. Solubility: The solvent should have high solubility for vanillin at high temperatures but a low solubility for vanillin at low temperatures. This property allows vanillin to dissolve completely in the hot solvent during the recrystallization process, and then form crystals as the solution cools down.

2. Selectivity: The solvent should selectively dissolve vanillin, leaving impurities such as other compounds or by-products less soluble or insoluble. This selectivity ensures that the vanillin crystals obtained after recrystallization are pure.

3. Volatility: The ideal solvent should be easily volatilized or evaporated off once the recrystallization process is complete. This makes it easier to recover the purified vanillin crystals.

4. Non-toxicity: Since vanillin is commonly used in food and pharmaceutical applications, it is essential that the solvent used for recrystallization is non-toxic and does not introduce any harmful contaminants.

5. Inertness: The solvent should be chemically inert towards vanillin, meaning it does not react or interfere with the properties of vanillin during the recrystallization process. This ensures that the purity and properties of vanillin are preserved.

While maintaining a cold temperature during recrystallization can be beneficial, it is not a characteristic of the solvent itself, but rather a condition used to control the crystallization process. Cold temperatures expedite the formation of smaller, purer crystals, but the solvent chosen still needs to have the aforementioned characteristics.