I don't have any melting advice.
What I can say is that the low coolant sensor that goes into the radiator is a failure point for these cars. I've disconnected mine (after replacing it only to have the new one fail shortly after installlation). This gets rid of the stupid low coolant light.
Also, the drivers side will blow warm when you're low on freon. 9/10 times the belng motor is a red herring.
Believe me - I tore apart my whol dash on this only to realize that it was a complete waste of time. When you're a little low on freon, you will get cold air on the pass side and warm on the driver's. Search the forums for blend motor or the like and you will see what I mean.
Before you waste any time on a belnd motor, pickup a can of freon. I bet it fixes your issue.