Mac mini havte one off the most advanace colling system insalled in it. Its not a good idea to putt any off such appliances in the refrigerator. Mini refrigerators works like the others bigger size refrigerators. Although you can use a cooling fan in your room to keep the environment cool.
We have one of these portable air conditioning units in each of our computer rooms on 12 different sites, efficient and low cost purchase. Its the first thing fitted when a new room is commissioned.