Two ideas, not that I know where your fan is or if you have one.
While in the Tropics on our sailboat we used reflective insulation as a sun-shield. Although the refer was insulated heavily--built properly-- the insulation hung over the side made a significant difference. At times, we used the insulation for our windows even though they were bronze coated and reflective. Anything helped.
Today, our RV is sometimes enhanced by this sheeting on the inside of our windows which makes a huge difference in the 5w temp. You'll be able to feel the difference no matter the curtain style. And in Alaska this insulation blocked that 22+ hours of light in our bedroom. If it's hot inside the cabin your refer will work harder.
However, since we've got some space between the refer and the RV outside wall, with a bit of work this reflective insulation was added. I'm uncertain if we could measure the difference since it was done on day one, but it is bound to help while staying put in AZ, TX, etc, especially if the sun is on that side.
BTW, there are several model fans which are sold to mount between the wall and refer, exhausting hot air, but they take power.
Finally, we've always used a small 3v fan inside the refer to circulate the air. Measurements of the refer confirmed it's worth.
A product from Home Depot, Model # BP24010 Store SKU # 184928, might give you some ideas.