For a case to have the coolest airflow, must the exhaust be higher than the intake (warm air rises, cool air sink, etc)?

At the rear of my case, I have the power supply fan and the case fan, as the exhaust. These are both in the upper half of my case.

At the front bottom, there are six tiny holes, which I think may even be negligible. The real intake for computer comes from a staggered grid of small vents on the side panels on my computer. They span almost the entire height of my case, and are towards the front.

How smart (or stupid) would it be to cover the upper half of the side vents, so that the intake comes from only the bottom? Shouldn't this [theoretically?] give me a cooler air flow?

Thanks.

This is a neat idea but I believe it will not benefit your cooling because the air which is outside the case that is about to enter the vents is the same temperature 1" above the case bottom as it is 1" below the case top. That is, the temperature of the air in the case may vary from bottom to top, but the temperature of the air in your room isn't going to change over a height differential of 1 foot. Unless maybe your case is right on a cool floor.

The second law of thermodynamics guarantees that your exhaust will be hotter than your intake.