possible alternator issue or battery?

[awd-drifter]

Well, just yesterday night I was coming back from work. I had the HID lights on and suddenly they went off. Car was still driving perfect, lights on dash did not dim. Luckly my house is about miles from work. I open the hood and see if the HID failed on me...nope, Battery is spitting out it's liquid, not a huge puddle but small enough to blame the battery.
Here's the thing though, I was just taking it for a drive today(no HID, no dash dim) and while on a small highway, my thermo gauge went near the first line of the "H" mark. Left the car to cool down for about 4 hours and checked my coolant. Coolant is still FULL. Weird thing is that whenever my volt gauge is full (14volts) during highway cruise, the thermo goes near the 1st line of "H". When volt gauge is at 11-12 volts, thermo goes back to normal. ??? I just replaced the Alternator 2 weeks ago. Battery is leaking. I'm putting my money on the battery, but i need help just to make sure it's the battery and not anything electrical. Thanks!

Cliff Notes:
- Thermo goes to "H" when crusing @ full alty voltage
- Thermo returns to normal when alty voltage is at 11-12
- Battery is spitting out it's liquids