If the pump is designed to kick only when hot then the circuit is gravity. An airlock is a possibility.. There is a chance that the pump is doing little or nothing to assist circulation if there's a lot of air trapped in the gravity circuit. It may well be just circulating water around the radiators, bypassing the boiler all together
The take-off for the pump is crucial if it is to be of any benefit in assisting the removal of the heat from the boiler.... You use to be able to get something like an injection tee or swepped tee that would aid the gravity circulation when the pump was operated ... It's been a long time since I've had much to do with gravity circs.... Not sure if they're still available or in use and whether something such as this would help the circulation TBH! Depends on the severity of the restriction ...