I have a rectangular BLUE rubbermaid 50qt cooler and I usually will lose 2-3 degrees in the hour mash. That doesn't bother me and it seems to be the norm when mashing with a cooler.
As for cleaning, it was a little more difficult to clean when I was brewing in my kitchen. Brewing in the garage has made cleanup very easy. After dumping the grains and spraying out with a garden hose, I use the cooler to collect the initial hot water runnings from my chiller when chilling the wort. I then throw in some Oxiclean and use the mixture in the cooler to clean off other brewing equipment. When I'm finished, I dump the cooler, spray it out and dry it. Keeps the cooler clean and bright white!