Keep in mind that there is also only a narrow window of thickness where a steel company will offer the same grade as either hot rolled or cold rolled. This is likely only between 1.8 and 2.5mm.
Thin-gauge hot roll limits the tons per hour of the steel mill, so don't be surprised if there is a "gauge extra" in the pricing.
Thick gauge cold roll requires different hot band processing so that the cold mill can still achieve the approx 70% thickness reduction to produce the desired properties.
Bottom line: it isn't a guarantee that hot rolled steel will be less expensive than cold rolled steel across the board, or that it is even an option for your grade/coating/gauge of choice
-Danny