Here's the answer, after much head-shaking, and screwdriver-brandishing:
The ATI X700Pro (and Asus/Sapphire versions of same) all have a fan and heatsink which blows air 'up' the card, as well as along it. Especially if you're using a desktop or media-pc case, that upwards airflow gets blocked by the case, and the thing hasn't a hope of keeping cool.
If your case is set up for air to flow front-to-back (most are) the fan and heatsink is also trying to blow air along the card towars the front of your case, and thus against the flow. That's not too smart either, but a lot of NVidia and other ATI cards have the same design.
So, I took the plunge and ordered Arctic Cooling's ATI silencer. It's very easy to fit - a five minute job and far less tricky than I expected. It gets the airflow going the right way. However, you may have to re-think how your case fans are set up after you fit it - because it needs a lot of air to be at it's best, and with insufficient air, won't solve the overheating problem - I had to turn one of my other case fans around to make sure plenty of air was flowing in to the case to feed the thing.
And now? My PC is
colder when I'm gaming than when it's off. This I like.
However, absolutely no thanks whatsoever to ATI Customer Support. They haven't given me any answers to my questions, nor yet to a
strong suggestion that that redesign that stupid heatsink to save themselves a whole load of RMAs, and it took a week to get the Arctic Cooler, so they've had a fair chance. They're probably too busy worrying about their insider trading investigation...
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