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Surface area to volume is irrelevant. We're talking about how much cooling power it takes to compensate for the loss rate, not how quickly the vehicle will cool down after you stop cooling it. The loss rate is proportional to the surface area. The volume does not factor into it.
fun fact: this is why smaller animals like mice have much faster heart rates than larger animals. They would otherwise lose too much body heat and die in cold weather
That's because heat generation in mammals is proportional to their volume, which has absolutely no bearing on the amount of power needed to overcome the loss rate, which is, as stated, proportional to the surface area.