I would suspect a bad starter... could have dirty brushes or contacts and a weak one gets weaker with heat. Sounds like your battery and alternator are both okay. I've had similar troubles before that turned out to be a loose (not tight) ground connection to the battery... as was mentioned before, check your ground... from battery to frame and battery to engine block...

on your new voltmeter, if you had the settings or the leads setup to read current (Amps) you would have a short and burn your leads measuring across the battery posts...

goode luck,

-Chris