Antifreeze has a rust inhibitor in it, so if you run it with just water then you will get rust building up inside the water ways which will eventually cause a blockage in the system. I don't think it will be the cat, you will just notice a loss in power if that fails. It could also be worth changing the temperature sensor, it sits between number 2 and 3 spark plug. Check the wiring to it too for damage / breaks.

I'd also get the car up to normal running temperature then remove the radiator cap CAREFULLY, put a towel over the cap and release very slowly. Look in the tank and if there is a steady stream of bubbles coming up through, then i'd be looking at a head gasket issue.