A fan would introduce more noise, which I think is why they want to cool down their minis (because the fans are running constantly). What would probably work, although I don't know the technical name for them, are those inserts that you see in hot/cold coolers that either keep picnic food hot or cold. Placing one of those on the mini should absorb the heat like a sponge, especially if you cooled it ahead of time. That would be noiseless and functional.
Tec's or pelitiers are not the answer!