Does you computer have a good airflow? Memory needs to be cooled too, else it can produce errors. I can change my fan speeds and I had two modules that could show their temperature. When I ran Memtest, the first pass was ok, the second too but later it gave errors. I checked the temperature and it was above 55 C. When I turned up the fans (front intake and rear exhaust), Memtest ran for over 10 hours without any error. First thing to do is check your airflow. If you don't have a see-through panel to read the thermometer, you might want to open your case when you get errors and read it then. Of course, don't use any metal on the memory, as it might short.
With a see-through side panel, you can close your case and position the thermometer so you can read the temperature. There are different kinds of thermometers, so check the one that fits best. A laser readout is the safest, but can also be the most expensive.
Throw Apples out the Windows, but make sure not to hit the Penguin.