The diagram shows energy changes for a chemical reaction.

The diagram shows that the energy level of the reactants is above the energy level of the products. This means that the reaction releases energy to the surroundings.

A reaction that releases energy (where products have lower energy than reactants) is an exothermic reaction.

• A. The reaction gives out heat. Exothermic reactions release energy, often as heat. This statement is correct.
• B. The reaction vessel becomes cool. If a reaction gives out heat, the surroundings (including the reaction vessel) should become warmer, not cooler. A reaction that makes the vessel cool would be endothermic (absorbing heat). This statement is incorrect.
• C. The reactants have more energy than the products. This is directly shown in the diagram and is a characteristic of an exothermic reaction. This statement is correct.
• D. The reaction is exothermic. As determined in Step 2, the reaction releases energy, so it is exothermic. This statement is correct.

The question asks for the statement that is not correct. Based on the evaluation, statement B is incorrect.

The final answer is $\boxed{\text{B}}$.