I cant find a definite answer for this but is there any chance that a mechanical fuel pump could fail only when it gets warm? As in when the motor reaches operating temp.

 

System in general: the carb system's fuel lines run fairly close to the passenger side exhaust and heat can cause vapor lock, or more likely, hot fuel boiling in the carb.

ensure the return line is functioning properly and routing fuel back to the tank. you can check fuel return from the pump by removing the rubber return line and observing flow. you can also blow compressed air through the steel line back to the tank to ensure it is free of obstruction.

if the return system is not working, you will have hot fuel problems. even with it functioning you 'may' have hot fuel problems. later carb systems used an in-tank helper pump to combat this. it was also a retrofit option for GM service back in the day.

fuel pump specific: I've had a fuel pump fail so that it was not pumping efficiently enough to provide full flow and starved the car when hot. upon removal and inspection, the swaged fittings that hold the fuel pump's fulcrum had failed on one side. as a result the pump's 'lever' was not seated enough to provide full movement with the cam eccentric. it would 'pump' but probably not enough to flow adequate return to offset the heat. if that makes sense.