I'm not sure what you're asking. I think by "2 core" heater, they mean "2 wire", which most heaters are. Then there are usually 1 or 2 more wires for a temperature sensor. The heater core itself can also be used as a temperature sensor, but I don't know of any that do that. I'd like to hear of one.
The one you are referencing looks to me like it *does* have a temperature sensor.
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Edit: I think I see what you mean. It says it is temperature controlled, yet has only two wires. It probably is using the heater as the sensor. If J1 is the only connection (hard to read the schematic) to the iron, that would confirm it.
Sure, you could mod the controller for 4-wire. Measure the resistance at various temperatures for the two heater types. If they are close, it should work. Connect the heater and leave the sensor disconnected. It the temperature curves are different, the mod wouldn't be trivial.
Another possibility is that there's a thermocouple in series with the heater, but I don't think so based on the schematic.