Scooter stops working once it's warmed up?

Hello, I bought a scooter (Piaggio Typhoon 50, built in 2011). When I ride it, it runs fine for the first 3-5 minutes, then everything is normal. However, once it warms up, it won't go full throttle. When I give it full throttle, it runs, but doesn't accelerate, as if it were idling. Also, if I keep it at full throttle for a while, I briefly get a relatively normal speed for full throttle (about 5 seconds of acceleration, and then the speed is reached for about 2 seconds). What could be wrong? Best, and thanks in advance.