If you don't want a chilled one, ask for unchilled.
"noncold" doesn't occur because the prefix "non" of Latin origin does not usually combine with adjectives of Germanic origin: we do not have "nonfriendly", "nonhappy", but we do have "nonalcoholic" and "nontoxic". On the other hand, "non" is broadly compatible with gerund forms of verbs, regardless of their origin: e.g. "nonliving things", "nonsmoking area", as well as with "-er" forms related to "-ing": "nonsmoker".
Something that has not been made cold is also "uncooled"; it's just that the verb more commonly used for deliberately cooling a drink is to "chill": "Beer should be served {chilled | cooled ?}."
To address a question in the comments below: "nonchilled" is also awkward because "non" also doesn't combine with verbs at all, including verbs formed from nouns, and so it goes poorly with "-ed" adjectives which are derived from verb participles. "to nonchill" could never be a verb, and so "nonchilled" could never be a participle: "the weather had nonchilled" is nonsense which probably intends to say "the weather had not chilled". A counterexample is "nonplussed"; however "plus" is not used as a verb, "nonplus" is basically a unit and note that it's two pieces of Latin origin.