I had a similar problem a couple of months ago, driving in France. As soon as the speed picked up to around 75-80mph the steering wheel was visibly shaking. It disappeared after a 3 hour drive.
I think my problem was linked to the fact that the car is sitting around on the same contact patch on the tyre for days at a time and it had slightly deformed the tyre.
I think the long fast drive heated the tyre nicely and centrifugal force help to re-round it.
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