I often hear people say:
Do you want to go out this evening?
But it seems no-one says:
Will you want to go out this evening?
Do we often use "will want"?
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It would not be used as you have it, but it's very common. "Will you want an extra seat tonight?" ... "He will (He'll) want a good table." ... "They will (They'll) want 2:00 tee times." ... "She will (She'll) want something unexpected for her birthday." There is nothing unusual about this construction. Can you use the edit link to tell us why you think it is unusual? – P. E. Dant Reinstate Monica Oct 27 '16 at 3:01
Your butler, if you had one, might say
Will you want to go out this evening, sir?
Will is a helping verb that can be used in a future request that way. But in the above sentence it is a mannered way of speaking, and would be unlikely to be used outside a posh drawing room, say.
If the "want" refers to an item, however, you may well hear constructions like
Will you want the car tonight?
Will you want more beef jerky for when you go camping?
It's still a little bit mannered, but unexceptionable and certainly not drawing-roomish.
Remember, it's all about ascertaining what someone's future desires will be. In that sense, do simply doesn't work. When you say Do you want [something]? you're talking about wanting it right now. Granted, you could say Do you want [something] tomorrow? but that is not quite the right word here.
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Not to quibble, but I think you're a bit off on one detail. As it happens, the event-booking person at a restaurant where I had reserved a table, and mentioned that I wasn't certain about the number of diners, called and asked me: "Will you want an extra seat tonight?" It didn't sound mannered to me, especially in her thick Bronx accent that sounded like: "Wiyawannanextra seat." – P. E. Dant Reinstate Monica Oct 27 '16 at 3:35
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@P.E.Dant: That is a serving person, in function similar to a butler in that respect. – Robusto Oct 27 '16 at 3:43
