We've replaced the battery with new, and the car was fine, parked for a week, then driven again, and again it was fine. The next day, we found that the battery had drained to about eight volts. On jump start attempts, we can't even get the solenoid to click. In the start position, the temp gauge goes to max even tho the engine is cold. Where is hard to say.
Shorts are hard to trace down and requires a volt meter and a knowlege of electronics.
I believe the temp gauge maxing out in the start position is normal. It should return to normal when the key is released to the run position. That might be a place to look for your short.