I stop and buy a cold drink. Worth to get off the bike a few minutes rest and then continue on.
I have a small 6 pack cooler with a zippered top. I put drinks in it and then fill it with ice. it works so well that even on scortching hot days there is ice at the end of the day.
It sounds like what California Side Car put on my Escapade trailer. It is a nice set up, maybe they sell it the way you are asking for. It is a quality mount and cover over an everyday but good cooler.