Google Adsense won't let you do that, that's for sure. I don't know about many other ads clients, but I don't think I've ever heard of one that would allow this kind of setup.
One thing you could do is find search engines/websites that have affiliate programs. I forgot which it was, but there used to be a Dutch startup search website that would allow you to link to custom search queries on their page and get paid for clicks. Maybe there's more search affiliates like that, so you could just generate links to their search page based on the search queries used on your site.
Another option would be to register with some general affiliate brokers and set up your own database of affiliate links with related terms, so that when a user searches on a term you could query your database for that term and display affiliate links with the same terms from your database. This will take a lot of work though.
Finally, you could just optimize your search results page to contain the search query in the title, meta keywords and description, the
<h1> tag and a couple of times throughout your page. This way you might be able to trick adsense into displaying ads that relate to the searched terms, but it's in no way waterproof.