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This is just poor thermal design. You'd actually be using the radiator to warm the air as it comes in.
Errr...yeah? As opposed to blowing already warm air through the rad? Blowing some warm air through the case wouldn't be a enough to raise the temperature of the components.
I guess the difference is I don't see the warm air from the rads as being much of an issue because its really not that hot.
This is just poor thermal design. You'd actually be using the radiator to warm the cold air as it comes in.
But if you had the radiator outside the case, you remove its heat output from the problem of cooling the case entirely.
I accept that having the radiator on the edge of the case, with fans pushing or pulling its heat outwards is OK.