you may have blown the head gasket when it overheated. if nothing else take the two heater hoses lose at the firewall and hook em together with a connector and a couple clamps or plug em. if your issue goes away, after filling and bleeding the cooling system then you know its the heater core.

 

How's the oil level? Is it milky? Do you see and fluid around the head gasket and lower intake? Do you get heat out of your car?

 

Heat worked for about 10 minutes after we changed the thermostat; had not worked before then.

We're getting bombarded by this ice storm, so I'll have to check oil and those leaks later this week.

Also, engine sounds like a damn lawnmower, and is idling around 1500

 

well id say you got something more than a bad heater core. 3.4 does not take kindly to overheating. like freeze said look for coolant in the oil or leakage around the head to block area.

 

could be a pin hole in your rad. Had the same problem with my car steaming out around the rad cap and it turned out to be a pin hole.