I think the stock car pulley is too large in diameter, particularly once the engine has been upgraded, for adequate cooling.
The pulley affects two things which are required to cool properly, fan speed, ie air flow, and water pump speed, ie coolant flow. If you have too little of either, or both, it will not cool adequately at low speed, ie idle. A bigger pulley slows the fan and water pump, but requires less hp while a smaller pulley speeds up the water pump, but requires more hp.
For racing, a big pulley is fine. For the street, a small pulley is what you want. For street / strip, you are a little more limited and have to make a compromise - you want the ratio to be the same diameter as the crank or smaller but make sure the water pump stays under 7000rpm at the shift point.
Lawrenceville, GA