You shouldn't have to maintain a mash if it is in a cooler. You will have to bring your strike water up high enough to compensate for the grain and cooler being colder. When I use my cooler (10g igloo) I bring my strike water up to mash temp + some and use 4gal of strike water. The amount of the "+ some" depends on how cold the other things are. This time of year (in new england), I can use strike water at 162 to get a mash temp of 152. In the winter, I have to have my strike water closer to 170 to get the same result.
After mixing the stuff together in the cooler, I check the temp and then adjust with hot/cold water to get where I need to be. After doing it enough of them, you will be able to pretty reliably guess within a couple degrees.
Once things are mixed and at the right temp, I put the top on the cooler and might see 2 deg F change in 90 minutes. The cooler certainly shouldn't be losing 10s of degrees.
Remember, you have to compensate for the thermal mass of the grain and the cooler too (unless you pre-heat it).