Ok. So it sounds as if you have an active cooling system problem. A few possibilities are a water pump, or possible cylinder head gasket. Though rare I have seen where the impeller on the water pump comes loose from the shaft that drives the impeller thereby not pumping coolant and allowing the engine to overheat. Water pump replacement on the HHR is not an easy task and it does require some special tools for holding the drive sprocket since it drives off the timing chain. The other problem seems a little more likely and essentially what happens is that exhaust gas enters the cooling system from a failed cylinder head gasket. When the exhaust enters the cooling system it super heats the coolant and eventually the coolant boils. You can test for exhaust gas in the cooling system with a tool/test kit called a block test. There is a colored fluid that turns from blue to yellow when exhaust gas is present. This kit can usually be found at most local parts stores like Napa or AutoZone. There are instructions in the kit that you would follow to test for exhaust gas. The kits are relatively inexpensive. I would test for this before inspecting the water pump. If the engine seems to be consuming coolant but no external leaks are found, I would strongly suspect a cylinder head gasket failure. All of these tests are assuming you had the overheat problem before you changed the thermostat and flushed the cooling system. If the overheat has been a result of this previous work then I would suspect an air pocket causing the engine to overheat.