It's really not possible for the temps to jump around like that, so something isn't right.
When you mash in, stir thoroughly. Then check the temperature in at least three different places. If the temps are different, stir some more. Once the temperature is equalized throughout, cover and walk away. You can check it again, maybe once, to make sure it's holding the temperature.
As the others mentioned, preheating the cooler for at least 15 minutes with a hotter-than-mash-temp water will help hold the temperature and keep the cooler from losing heat.
Broken Leg Brewery
Giving beer a leg to stand on since 2006