You should also take into account that most engine components (block, head, tranny case) are all made of aluminum, a very good heat conductor. By reducing the airflow over their surface you'll make them heat up faster as well. It may not be a huge surface area, but its not small either.
Just to clarify, the coolant in the radiator has no bearing on warm up time (other than keeping the engine bay warmer which is a factor too). It is only used for cooling. You will never heat it all up to operating temperature. If you did, you would overheat the engine.
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