1997 Mitsubishi Montero Fails to start on hot days

Last summer around July of 2007 on a hot day I came back to my car after some quick shopping at the mall (aprox. 45min later) for a pair of shorts thinking I was going to go to the beach! Proceeded to turn the key but all I heard was a weak sound as if the starter lacked enough juice to crank the engine. I then cleaned the battery & cable terminals which had built some sulfur, hooked it back & voila! The engine started but then it reved down & shut down again. I then started the engine again but had to keep my foot on the gas so engine won't rev down and stall. Drove back home like this. (NOTE: I noticed that the car was anemic). Next day I took the car to Strauss repair. They indicated the car needed a tune-up & that one cylinder was mis-firing which is why the engine was weak. Picked up car the next day. They indicated that all electrical cables (except battery cables) were changed. Idling problem was gone but car was still weak. Surprisingly the car recouped it's power after a few days. I enjoyed the rest of my summer. Fast forward to May 08 & again on a hot day I came back to my car and same thing. The truck failed to start I checked battery terminals which again had formed white sulfur powder. I once again cleaned terminals, car was able to start but wants to rev down. I managed to take it to a mechanic who connected a volt meter to battery while car was running and it clocked-in at 12 Volts exactly. He said it needs new battery. I find it hard to believe this because every time after I clean the terminals it starts although it wants to rev down. Battery cables for this car are very expensive (about $120 for both) so if It's not the cables I wouldn't like to replace them.

Please shed some light.

Thanks in advance!

Xavier