If I was in your situation I'd try preheating with a couple gallons of boiling water, drain that, then put in strike water about 10* higher than mash temp and dough in. Give it one good stir then leave it till halfway and give another. The insulation on those coolers is good, the problem is the mass of air, over shooting strike water will heat the air and grain and leave you near mash temp. You may have to test out how much overshoot it takes to keep you near your mash temp. Beersmith may be able to help figure that out.