The little fan on the inside is to keep the temperature more even through out the refrigerator
. If the thermometer is in the bottom it may very well get warmer. But by using it you can keep from freezing things in the refrigerator
part of the unit.
Dometic instructions say, it will take 8 hrs for it to cool down. (Ours takes much longer) But you should be able to feel the freezer get cool and cold much faster. They also say it must be level to prevent damage to the unit. RV stores sell a small round bubble level for this purpose. Half of the bubble is suppose to be on the inside of the little black circle. Other wise you can cause permanent damage to the unit. Driving while on gas is OK because the motion shakes the unit enough to prevent the damage. But this is another good reason to have the trailer close to level when under tow, to help prevent damage while stopped for a few hours. And try to park in a rather level area.
We cool ours down with 110 all night before we leave on a trip. And everything is cooled in our house refrigerator
before it is put in. We even freeze the ice trays in the house.