Motorcycle Repair Questions? Ask a Mechanic ASAP
It is unlikely that the throttle cable is at fault here. The Carburettors are fited with an automatic choke that allows the starting of the engine in the cold. This will be operated by a spring system / vacuum system which allows the choke to remain in the on position when cold. As the engine warms up and the throttle is used the action of the throttle usage releases the choke at the appropriate time.
It may be that the choke unit is the issue with either a weak spring or leaking diaphragm on the choke unit causing the issue. I would check this out first using the appropriate service manual for your machine for reference.