1990 190E 2.6

Here are the events leading up to my current situation:

My car would die from driving continuously with a/c on, high speed aux fan on, radio on. I tested the battery and noticed that it would be at around 12.3....battery was only 1 yr old, but temp out where I am is 100+*F, nevertheless battery was relatively new. I had a warranty so I swapped the battery out for a brand new one, and I checked my voltage regulator which seemed like the 2 spring loaded bushings were quite worn. I replace the VR with a used one that was about 85% new. I replaced my belt tensioner, tensioner rod, and tensioner shock. Today while driving, again a/c on, high speed fan on, and radio on, ambient outside temp was 104*F, I noticed that my car began to pulse, ie, the idle was going up and down (between 5 and 5 and a half rpm steadily, like a wave) I switched on my lights (HID's) and they came on, but they were flashing on and off with the pulsing of the car. I turned everything off except for high speed fans because they were on automatically because my needle was at about 105-110*C. Continued driving and came to a light and car shut off. Got it towed to gas station, tested battery at 10.34v, jump-started car, took battery in to charge up, drove car home. all is well for the time being. Car does not die everyday, but on days when I am driving for hours in the city, not highway. and stopping and going, it seems as if the constant engine running in the heat with the load is causing either the alternator or battery to die. Does this sound right? Any suggestions on what the probalem can be? I had the battery and alternator tested and battery is of course good and all components of alternator (diode, voltage regulator, and one other thing they said) are good. I'm going to see if my belt is tight enough, but I did not hear any squeaking when driving. Sorry so long of a post, but I need help ASAP because I will be driving tomorrow under the same conditions. Thanks.

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1990 190E 3.0L