My 84 240 DL wagon is having a battery problem. The other day, as I was driving on the highway with the AC on, I noticed my engine temp was dropping drastically. Supprised, because AC should cause a slight increase in engine temp, I pulled over to see what the problem was. I popped the hood with the engine running and didn't see anything unusual. Like an idiot I decided to turn off the engine and restart. Well, the battery was deader than a door nail and I had to get a jump start. I have had the problem twice since then, and now am not running the AC at all. Does this sound like a good old dying battery or something more sinister? The positive battery was corroded pretty badly so I cleaned it with baking soda about two weeks ago. Now it is corroding again. Any advice is welcome. Thanks.

PS. I figured that the temp gauge was dropping because it must be dependent on battery voltage to function properly. Does this make sense?