I've had the same problem with my 5 gallon cooler HLT. Some people spray foam insulation (Great Stuff) into the lid to help prevent heat loss through the top - I tried that but the foam collapsed and turned into liquid, so that didn't work very well for me. I have taped a piece of Reflectrix to the top and wrap the sides with a blanket which helps a lot.
I don't know if you will be able to use the following method on your system, but here's how I do it:
I've heard so many stories of coolers warping and cracking that I am really careful to heat mine gradually. I heat my water in a kettle on my electric brew stove and pump to my 10 gallon cooler MLT using my March pump. I start pumping at about 100 degrees - pump a bunch of water to the MLT, then turn off the pump (I have a conveniently mounted toggle switch) and let the water drain back through the pump into the kettle (takes a few minutes to drain back). By the time all the water is back in the kettle, it is about 20ºF hotter than before (I'm still heating the kettle), so I pump the water back to the MLT and drain again, repeating in 20ºF increments until I have reached about 165ºF, at which point I pump my desired amount of strike water to the MLT. Then while I'm waiting for the MLT temperature to stabilize before I dough in, I repeat the whole process with my HLT, heating up the sparge water to about 180ºF and I leave at least a gallon of empty space in the HLT. While I'm mashing, I heat up two or three gallons of water to boiling for mash out water, and just before I mash out, I pump enough of the boiling water into my HLT to heat the sparge water back up to 180ºF or whatever I need for the particular grain bill. Because I single batch sparge, the water in the HLT hasn't cooled too much by the time I finish the mashout and drain the first runnings and I'm ready to sparge.