Why carburetter setup can affect hot running
Carburetters control how fuel and air are delivered to the engine. When the mixture is wrong, the engine can still run, but it may run hotter, rougher or less efficiently than it should. That makes cooling diagnosis much harder, because the temperature gauge points at the radiator while the real trouble may be hiding on the inlet side.
Inlet air leaks can create a weak mixture
The gaskets between the carburetter and inlet manifold, and between the inlet manifold and cylinder head, must seal properly. If these gaskets deteriorate, the running engine can draw in unwanted air. That extra air alters the mixture and can make it too weak, which can lead to hot running.
Worn carburetters can have the same effect, especially around the butterfly throttle shafts. If the shafts are worn, they can let additional air into the intake mixture. That can make the engine run hotter even when the cooling system itself is not the main fault.
Too rich can also cause damage and heat
A weak mixture is a known hot-running cause, but a rich mixture should not be ignored either. If too much petrol enters the combustion chamber, not all of it can be fully burnt during combustion.
Excess petrol can remain in the cylinder and wash oil from the bore on the downward stroke. This bore wash reduces lubrication, increases heat and, over time, can accelerate piston and bore wear. It can also dilute the oil in the sump, which is another fine way of making a simple diagnosis less simple.
Exhaust manifold leaks add heat where you do not want it
If the gasket between the exhaust manifold and cylinder head deteriorates, hot gases can escape into the engine bay. That can raise under-bonnet temperature significantly, adding heat around the engine, carburetters, fuel lines and cooling system.
Before replacing major cooling parts, inspect the carburetter, inlet and exhaust sealing carefully. A sound cooling system can only do so much if the engine setup is adding heat from the other side of the argument.