Thanks Loubapache. If push came to shove, I would have wagered my Ph.D. (Physics and Applied Mathematics) on it!
I can think of other reasons why you would want the head cold (in addition to those I listed above). Since hot aluminum has a lower density than cold aluminum, it would be more likely to be galled by the steel plug.
Also, depending on how hot we're talking about, you wouldn't want the cool air rushing in and hitting a red-hot exhaust valve.
So, there are probably lots of reasons, but it sure isn't the diameter of the hole!