Trapped air usually happens when the heater core is higher than the fill on the radiator. Minivans and some SUV's have this as a common problem. The vehicle here is a grand prix and this should not be a problem. If they have been driving the car without leaks (so no air gets into the system)...
A couple of (not so) quick comments, A plugged radiator will not stop you from the heat but will overheat the engine, The high rpm before feeling the heat is a typical sign of a water pump going bad. two quick checks for that is to get a mirror or look from under the vehicle (or if you can see...
Quick question, does the phase transition of the ice melting help or hinder the cooling process? If I remember right, it helps with the chilling effect. And if so, will insulating the ice in any material ( I like the gold plated copper idea) hinder this?