Far be it from ME to want to save Toyota from getting a reputation for bad batteries, but especially since this is the second battery to go bad in the same fashion, do yourself a favor, and humor me, get someone to tighten the alternator belt, or replace the belt, and check for free play in the water pump pulley.
Unless of course you are having the Toyota dealer's techs do this repair, in which case, after the first call it all ought to be a warranty of the first battery anyway, since they should be well trained enough on the #1 brand of forklifts, to know to make these checks without us having to suggest it to them..