Modern Vespa

Hi everyone!
I recently purchased a Gt200 Vespa with 34000 kms on the clock and noticed the following issue.
After a few kms of ride the collant temperature right in the mid way on the gauge but when I park it and let the engine run for 5 more minutes the pin starts to move up to the 3/4.
Is that normal with these machines or I have a big issue?
Thanks for the answers in advance.

If you're stopped and idling the engine, eventually the temperature will rise high enough that the fan comes on, with the gauge needle at or above 3/4. It's only when you're moving that air normally gets through the radiators to cool things down.

So your situation sounds very normal!

I'm curious why you'd want to idle the engine like that though.

Is the cooling fan working?

Thank you for your answers. I just had a heat sensor problem before so I changed the sensor therefore I tested it under any possible circumstances and maybe payed too much attention to it.
I haven't had the fan turned on at this point but I thing it supposed to turn on when it reaches the 3/4 line.
Thank you for the responses hope everything will be fine with the bike.

Also be aware the fan switch is completely separate from the temperature gauge sensor.