Strange vibrating issue

I own my Prius for 6 weeks or so. It has 129.000 km (80.000 miles) on it.
I bought it with worn tires, so I knew I had to replace them soon.
With these bad tires, the car (steeringwheel/chair) vibrated while driving between 35 and 80 mph. Since the car needed new tires, I expected this vibrations to disappear with new tires and balancing.

Since a few days now, it has new tires and the wheels have been balanced.

Withing 200 meters from driving away from the Toyota garage, I felt the vibration, still. I went to the highway and confirmed that the vibrating was there within speeds of 35 and 80 mph.

Called the dealer, they suggested that maybe a balancing-lead had fallen off. The car will be returned to the dealer on monday for that.

What confuses me is the behaviour of these vibrations. They are not there all the time. Sometimes it vibrates instantly after a cold start (above 35 mph), sometimes it starts vibrating after a 15 minute drive.

Yesterday, I did this experiment:

Car was cold, I checked the pressure of the tires;
I start driving, 10 minutes abt 35 mph : No problem;
Then 5 minutes between 43 and 50 mph : No problem;
Then 5 minutes 35 mph : No problem;
Then 10 minutes 45 mph : No Problem;
Then 5 minutes highway, up to 75 mph, still no problem;
I took the exit, so had to slow down and to turn to return;
I went on the highway again, speed went up from 25 mph to 75 mph, and while the speed gets higher, I felt the vibration coming in steering wheel and chair.
I drove 75 mph for a minute or so, the vibrating stays;
I had to slow down, so I went gradiently from 75 mph to 43 mph and felt the vibration getting havier.
At 43 mph, it's the most noticable, but between 30 and 80 mph, it's there.

This experiment could indicate a (tire) temperature issue, but notice that at some occasions, the car (cold) vibrates directly when starting a trip.

Surely I will return to Toyota to check the balancing, but I'm not confinced at all that it has to do with that: Why does it not vibrate all the time when reaching the speeds where it vibrates? There are trips where it drives smoothly.

Thanks.