Power loss

Sorry, but this is a question on behalf of my grandson and it concerns his Vespa-type scooter which runs great for about fifteen minutes and starts to lose power. After it is shut down for awhile it starts and runs fine for another fifteen minutes and loses power again.

Does it do it more or less when it is cold and or hot? How is the humidity were you are? How old are the spark plug(s)? My guess is whatever passes for a coil is overheating.