Also ignition components wearout n become hot..if runs ok when cool then thats proof. U mite want to inspect cooling system or put amsoil radiatorboost in to run coldr
Inspect n clean all ignition parts. If bike has kistartr..replace batt w acapacitor sold at harleyshops. No mor batt upkeep or failure. Bike will start lika lawnmower
Things to check:
So we need three things for the engine to run,
1) Air
2) Fuel
3) Spark
Timing of these is essential and the assumption is that the timing is correct.
Sounds like you have two of three, air and spark however the fuel seems to be restricted. From the description it sounds like the engine runs until the fuel in the carburetors is gone then a trickle of fuel eventually fills then up over time.
Check that the fuel line flows enough fuel to keep up with the needed.
take a look at this youtube it is for swapping out the fork but he changes the seal so he has to refill it and then you see how to check the level. good luck.
https://www.youtube.com/watch?v=xfT49mEgzmM
The most likley cause of your problem is that the radiator fan is not running or turning on. Easy to check, run the bike untill the coolant bubbles out and listen for the fan. If you put your hand in front of the rad it should try to suck you hand toward it. If yhe fan is not running than you wither need a new fan or coolant temperature switch for the fan. It should be located in the head of the engine.
The internal design of a motorcycle ignition switch is typically complex and often is at least two independent switches working together. Where electronic immobilisers are concerned there is sometimes an in-built resistance the system must "see" before it will work.
Bypassing the switch safely would not be easy even with a wiring diagram and truth table and I suggest you don't try.
There is a cap on the right side of the crank that you remove and you can see the rotor with T and F marks and a notch on the cover housing for setting the timing.