OK, first up one comment: Good idea to edit your profile "Location" and make it clear you're
not in the US. Otherwise you'll get advised to just pick up something from NAPA, Pep Boys, Schmucks, Kragen, O'Reilly's etc...
You're stuck with some similar speed crimps to Australia.

Besides the lack of a fan shroud, there seem to be certain speeds where airflow through the underbonnet is poor to non-existent. It's a function of the body design and turbulence generated. Chances are, that low speed limit is contributing to your heat issues.
The sender for your temperature gauge is located on the passenger side (if it's RHD) of the cylinder head, near the back. Look for something resembling a tiny spark plug with a wire plugged to the top of it. Experiment with the engine running, disconnect the wire and see if the gauge moves, then dead short the wire and see if the gauge moves.
It's not an accurate piece from the factory so don't trust it too far. You can be reasonably confident that it shouldn't go far past halfway when the engine is in good shape.
Be suspicious of the ignition system unless it's truly been gone through. Retarded spark can cause overheating, too.
The bad news about parts is that very few things are likely to interchange with local supplies. This will have you cursing as you dig deep at times for minor things, and other occasions, looking to local restorers/machinists for convenient and pragmatic resolutions. Can the radiator leak be soldered?
If it's duff, you might be looking at a three row copper/brass radiator from one of the Mustang specialists. You can run over USD$500 for an aluminium unit, but they're really made for a V-8 and there would be minor hitches to adapt it in.
Regards, Adam.