Magneto is number one suspect. Try it with the end cover off, in case some electrical fault is grounding the magneto. This isolates a handlebar cut out switch. Check for a good spark, but also remove the pick ups, make sure the brushes are OK, and move freely. Clean the slip ring (clean rag on a stick, don't put your finger in.....a good mag will give you shock).
Reliable starting when cold, but a bit of a pig to start and/or mysterious cutting out when hot is typical of a failing condenser. An easy fix these days thanks to a very clever piece of modern technology.
You may be lucky and it is simply a fuel blockage, caused by rust or sediment being disturbed after long time standing. A cheap inline fuel filter is well worth having, it's far easier to swap a clogged filter than strip a carb, and a see through one lets you know if fuel is flowing.
Swarfy.
