The "baddy" doesn't have to be cool and illogical. The cold and logical mind can be just as terrifying in the right (wrong?) circumstances.
To quote H.G. Wells (from near the beginning of
War of the Worlds): "Yet across the gulf of space, minds that are to our minds as ours are to those of the beasts that perish, intellects vast and cool and unsympathetic, regarded this earth with envious eyes, and slowly and surely drew their plans against us. And early in the twentieth century came the great disillusionment."
The thought that this might be occurring in my world makes me feel warm and comfortable, I don't think.
