Does that mean you can't fabricate an ice sculpture out of ice or a snowman out of snow?

I think the "finished product" probably should be at whatever temperature we associate with that thing as a "finished product". "a pizza", for example, would be warm - assuming the caster had the skills to make a good pizza. Some objects have a temperature as part of their essence of being "that thing" and if you change them to be room temperature, then they're no longer that thing.

As for "the caster needs to be a proficient chef" we're covered. Konsi is a proficient chef. Personally, I wouldn't allow this for a caster without cook's utensils. (they could make sandwiches though)

As always, check with your DM. People are going to interpret this differently.