The slide holds the thermistor...it runs from the refrigerator through the back wall of the refrigerator to the control board of your refrigerator and does, indeed, control the temperature inside the refrigerator by regulating the on/off cycle of the burner/heater.
To make it colder, you want to slide the holder up on the fins of the cooling block and to make it warmer slide it down. Cold air sinks, so, moving it up will put it into "warmer" air and make the control board kick the burner (if on propane) or the electric element (if on shore power) on.
If your refrigerator still isn't getting cold enough, you can try moving the slide towards the right-most fin on the cooling block. If it is towards the middle, the thermistor will read cold air on both sides of it from the fins on each side. By moving it towards a fin more towards the edge of the cooling block, the thermistor will read warmer air along one edge and may get you another degree or two in "coldness". Just be careful on how much "tension" is on the thermistor cable; you need to allow some slack to allow for expansion and contraction with the temperature swings from off to full on. Doesn't need much, but, you don't want to string it tight, either.
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)