what you're seeing is the principle used in the ground heating/cooling systems, the temp in the ground tends to be stable year 'round, day and night, so the basement temp is less affected by increased summer air temps

don't think you'll get much out of it, but remember that warm air rises, cool air sinks .... if you vent the highest area of the house outdoors, the warmer air moving out will draw some amount of air from the lowest open space you have, which might be the basement stairs, especially if the basement door is ajar, and having that open at night when outdoor air is coolest would help keep the basement cool .... you could also set up some ducting to convect or fan force more of the cooler air up, but too much and you'll eventually heat the basement by drawing in daytime warm air from outside

Bill