I cover the whole cooler since it's so damn cold in Chicago.
The beauty of the velcro is you can cover as much or as little as you want. In your situation, I'd make a cover that fits the whole cooler and then cut it in half horizontally. If it's hot out, take it all off. If it's mildly cool and your temps aren't coming up, cover half. If it's really cold, put both halves on.
Or you can just start with a full cover on or off and see how it goes. You have options!