Effect of cooling a DC power adapter with too few amps?
The correct answer is, "find the appropriate sized adapter."  A quick Google search found them for $6 and up.

Your underpowered fan will not operate efficiently, leading to downstream heating problems that you're not considering.

Cooling the outside of the adapter is only half the battle.  You need to worry about thermal transfer from the transformer inside the adapter to the outer casing.  If the adapter can't move its internal heat to the surface fast enough, it doesn't matter how cold you get it.  It will eventually burn up.

If you get lucky and there are no downstream consequences and the adapter can cool itself fast enough ... then you've come up with just about the most expensive solution to the problem I can imagine.  How badly do you want that brew?  Remember, the correct adapter is $6+shipping.