Pointing the output from an A/C unit into the computer will work to reduce the ambient temperature inside the case, and as such will make everything run colder.
A word of caution regarding condensation is necessary however. If the components are hot, and they meet very cold air then condensation will form. This condensation will cause water droplets to appear on your motherboard and anything that gets warm.
There are two solutions to this. The first is to insulate the vulnerable parts with special waterproof coatings, this is messy and needs a lot of care with it's application. The second way is to not try to reduce the temperature so much as to allow condensation to form.
The amount you can get away with depends on a lot of factors, especially how much moisture is in the air. If you live where there is high humidity, you might only be able to reduce temps by a few degrees, in a drier climate, up to about 10c could be possible.
One way to test this is to fill a glass with water at around 60c and place it in the path of the cold air, this will illustrate the risk for your particular environment.