The term "warm market" refers to a group of people who have already shown interest in your product/service previously, or something similar to your product. This is the group of people you know are interested in your product/service and want more information on it. They have shown this interest by opting-in on a lead capture page, reaching out to you for questions or requesting more information.
When interacting with your warm market, you'll want to use different language and deals to keep them engaged with your product than you would with your cold market.