[LX5liter]

Check the heads with a straight edge before you replace them. It doesn't sound like a head warpage problem if you don't have any leaks or water in the oil. You probably already have the heads off by now so check the gaskets out thouroughly to see if water was leaking into the cylinder. When you put it back together it doesn't hurt to jack the front of the car up when you fill up the rad. This will help get rid of the air pockets. Anti-freeze is a good idea, it not only raises the boiling point of the water but is a rust inhibitor. without it you will be replacing your rad sooner and coolant passages can become restricted.
If you can't use anti-freeze there is some other products out there like " Water Wetter " that are track legal and may help out as well.

I hope you find your problem!