Posted on May 17, 2011 at 14:23You must have a shorted pin/ball, the RTC VBAT should be pulling uA's (ie close to a million less than you suggest) by itself. It's getting hot because there is a problem, to the point you may well have damaged the part.
Try connection only to the VBAT, use something like a BAV70T to split between the primary and backup supply.
You might want to xray/inspect how your part is attached/soldered, reevaluate your circuit, and replace the current part, as the amount of current you are describing has almost certainly destroyed the part, or some portions of it.
