The value of Kw decreases as the temperature decreases. Is the auto-ionization of water exothermic or endothermic?

Hi,
I am stuck on this question and would appreciate some guidance. The question states " The value of Kw decreases as the temperature decreases. Is the auto-ionization of water an exothermic or endothermic reaction in the forward direction?"
I feel like the answer should be exothermic as I know from studying Le Chatelier's principle that a decrease in temperature favours the reaction to occur in the forward direction. Is that a correct assumption?

Yes that is correct assumption;

Decreasing temperature will drive this reaction forward .This only happens to balance out the equilibrium: The reaction will shift forward to produce more heat. 

The Kw value represents the dissociation of water equilibrium:

H2O <----> OH- + H+

The Kw = [OH-][H+]  ( and it is multiplication of the concentration of the products)

if  Kw is increasing, it means that the concentration of the products increasing,which means forward reaction. 

Because heat is something the reaction produces, it is exothermic (meaning heat is released as a product).