You said it yourself, the temps aren't rising above 180 correct? At 180 your thermostat opens and that big ole cooler of yours starts to come into play correct? The cold running will be the same and it heats up to the 180 like it would regularly correct? Let's stop the heat from being removed from the system after it 'warms' to the thermostat opening temp. Baby bottle warmers and stuff seems like way too much work if while driving, the cooler will remove the heat that you were trying to get into the system. It seems that it is restricting you to the 180 range. Make sense? That's why covering/blocking airflow of the cooler seems simple yet effective.
Tell you what. Give it a try for a couple of days and see what happens. Nothing to 'engineer' into the system and it will cost you more in time than materials and specialized tools. If it works, great! Problem solved. If it doesn't, call me a moron for suggesting that something that simple and inexpensive would work
Have fun!