Hi David,
A heat shield is a good idea, but Bill is right, in this case it might help a little, but probably not much. The temps underhood continue to rise in the still air, for a while after the car has stopped. It's different with every car, depending upon a lot of factors such as how well the engien compartment is sealed and how efficient the cooling system is. The heat shield is more intended to stop radiant heat when the car is running and in motion, and air is moving around in there and being exhanged for fresh, cool air.
You are probably already aware, many modern cars have electric fans that are designed to run for a couple minutes after the engine is shut off, to address this problem. These fans will reduce underhood temps as quickly as possible. If your car has an electric fan, it would be relatively easy to set it up to function this way. Just connect it to a circuit that is hot all the time and use a thermo-switch to control it.
Some things you might check are the float bowls, if there is any leaking or the needle valves are working properly. It could also be a sign that the fuel pump, assuming an original one, is starting to get tired and is in need of a rebuild.
An alternative is an electric fuel pump, which will pressurize the system the moment you turn on the ignition, doesn't have to wait for the engine to start cranking. A small pump like a Facet can be hidden under the car or in the trunk and can be plumbed through the original pump, so that the car's originality is preserved as much as possible. With Facet or any electric fuel pump, it's important to check that the pressure is not too high, or flooding might the result. 3.5 to 4psi is all that's needed. A pressure regulator can also be used in the fuel line, to lower the output, if necessary.
Hard, hot starting might indicate a problem with the carbs, too. For example, this could be a choke that isn't fully off, due to adjustment. Or, it might be tied to carb synchronization or other issues. A general tune-up (adjust valves, go through the ignition, set timing, change spark plugs, etc.) might be a good idea before fiddling with the carbs, though.
Let us know what happens.
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