Not sure about your freezing issue, but 040's do run hot for sure (which is perfectly normal).
I'm assuming there's no damage around the battery area of the 4000 motherboard due to battery leakage? Any discolouration visible?
If you suspect it could be heat related then I suppose a dodgy solder joint can't be ruled out. Try using a room fan or something to properly blow air on the cpu card and motherboard together - see if it delays the freezing.
Have you had the machine re-capped? There's a chance an invisible leakage could have partially eaten through a track or something (could be under an an smd capacitor you see, leakage hidden). Any sign of dull solder joints on or around any of the smd caps? I suppose all A4000's should be re-capped by now (if the owner is sensible). To me, freezing does sound like CPU card issue.
Good luck, I hope you can get her working soon.
