Long time ago (1970 something) had a customer car with thumping & vibration for first couple minutes, but only when it was cold. Always stopped before he got it to the station, about 2 -3 miles. Turned out there was water inside the tire that froze at night, but melted as the tire heated up during use. Don't expect that has anything to do with your issue, but you reminded me of it. Was a pain to figure out, but obvious when resolved.
Tom, ice in the tire??? Now that's an interesting story! And at least a good excuse to build a heated garage... or move to Florida!
Dumb question, but does it have bigger tires? I ran into this with my '68 with negative-offset wheels. The tires would rub and "knock" in certain conditions. Just a thought.
Hotrod, No such thing as a dumb question when trying to diagnose a car problem...
But, no big tires. The car is pretty well stock, and so signs of tire rub, either.
Again, shocks are definitely part of the problem, but I'm not convinced that is all of it. Neither is he. When he gets it on the lift, he's going to look at bolt connections and bushings.
Maybe he'll get lucky and it is just a bad shock.
Thanks to all!