Not sure if this applies in your situation, but do not let the thermometer touch the sides or bottom of your cooler during the reading, it will read too cool. A good insulator will not allow for a lot of heat transfer between the hot mash and the outside. I use a 10 gal Home Depot.
Here is what I do: I never preheat, just dump in the water then the grains. Then I mash in for a minute, then take a reading. Stir the thermometer around a bit, make sure you are not in a hot/cold patch. Once I think the temp is satisfied, I close the lid and walk away for 60. I used to stir more frequently, but I have had my best results with a set-it and forget it approach.
Good Luck