I have a Carlin hot air oil fired system. The burner appears to short cycle when the stat calls for heat. Once the stat calls for heat the burner fires up and runs for a few minutes after the fan comes on. Then the burners shuts down for a few minutes while the fan still runs and fires up again. This cycle continues on and off until the stat is satisfied. My understanding is that the burner should continue to fire while the fan runs until the stat is satisfied. Then the fan continues to run until the heat chamber is cooled to the temp of the fan limit switch. Is this short cycle correct? What can cause this condition.

The fan high limit control could be out of range due to old age and to many cycles.
The oil burner could be over fired(to big a nozzle.)
The thermostat heat anticipator could be out of adjustment.
The air filter could be dirty.
Some of the registers or cold air returns could be blocked or turned off allowing excessive heat build up in the combustion chamber turning off the burner until the temp drops allowing the burner to come back on.
The operation you describe is not normal.