1981 Deville with overheating/dead battery issue, why?
 

I have an 81 Deville sedan with 74,000 miles. This car sat for the last 12 years undriven by the original owner. Because of this I have addressed matters that would occur from a car being unused so long and I have given it an oil change and a new air cleaner, and the radiator was flushed and filled. It also has a new thermostat and alternator. Problem was yesterday driving around in outside temps in the low 70's it overheated twice. This is odd because weeks ago after the fresh thermostat I was driving around in upper 80s temps no problem. Each time the Coolant Temp (not engine overheat, just coolant) light came on I pulled over and stopped, the radiator sucked all the antifreeze back in from the jug and the car drove some more. The second time I thought I would do the car a favor when it overheated so I pulled over and turned off the motor but I blasted the heat at 90 degrees to draw off heat from the engine faster, which I think killed the battery. I got the car jumped but later my Check Engine light came on and my dashboard lights got all blinky and then very dim so I pulled over and from a 2nd jump I got to drive home and today my car is dead as a doornail. I am pretty sure the battery is no good if it can't hold the charge from a brand new alternator, but why does the car overheat still? Its had a flush and fill and a brand new thermostat. I did notice the hose from the jug to the upper side of the radiator is full of fluid while the return hose from the lower point of the radiator is empty and hollow feeling. What is the matter with my Deville-any ideas?

Engine specs
 

Like my screen name alludes to this Deville has the 6.0 368 in V8-6-4 with the fuel injection, not the carb.