If it's a cold start issue only it won't be heat soak.
Check the choke operation, the jet nozzles should be all the way down. To test pull the choke on in the car, then in the engine bay reach under the carbs and see if you can pull the jet nozzle on each carb down any further. If you can they are sticking, you aren't getting full choke and cold starts will be hard. Try lubricating them when they are fully down, it worked for me many years ago.