In adol condensation if there is no heat in the reaction,will the elimination of water still happen? I mean without any heat is the product beta hydroxyaldehyde or an unsaturated aldehyde?

...Please post the question.

It is a reaction between benzaldehyde and acetone in the presence of NaOH and H3O+, but there is no heat.

The thing that you need to realize is that the Keto form is the most stable form. If there is not heat but it can lose H20 and form the double bond that will be stable with benzene then it will form. The final answer should be a stable double bond one carbon away from a ketone.

The reason why there is no heat is because of the benzene. When the reaction happens with a benzene in that position it doesnt need heat due to the stability of the alkene because it is conjugated together with the benzene.