We're in Texas. Today is going to be 102F at least. Our 14 View Profile came with a Coleman Mach 8 15.5 Btu heat pump with a BLACK bonnet. The Mach 8 is not noted for being a quiet unit. It is a NOISY BEAST! I discovered that there is a revised fan available that will reduce the noise and as usual a simple fan swap ended up being a more comprehensive upgrade. So my effort was not necessarily focused on creating a cooler working environment for the heat pump but simply on noise reduction.
BACKGROUND: The bonnet is very thin flexible (resin?) material. You could probably bend in in half if you dare. It does not have any reinforcing 'ribs' on the inside to provide strength.
So, it's like a drum head and will vibrate sympathetically with anything going on in the unit, e.g., the compressor and the fans. I also discovered that the bonnet rests against part of the compressor transmitting more vibration to the bonnet.
The additional benefit of adding damping material to the underside is that it provides thermal resistance and will reduce the solar effect on the unit's operation.
There are lots of expensive sound deadening materials available. At the suggestion of a local shop specializing in car audio systems, I used aluminum faced butyl roofing tape. The theory is 'mass damping...' Just like you do on a car door, trunk lid or hood to sound deaden vibration the large panels.
I upgraded the fan... easy work. I found a good 'take off' bonnet in white. Then applying the theory of 'mass damping' to the underside of the bonnet I covered in with the butyl roofing tape.
When completed the bonnet was significantly heavier and less flexible and less prone to induced vibration. Getting to the point, it is now covered with a heat reflecting material to keep the inside of the unit a bit cooler.
Additionally, I used aluminum HVAC tape to cover the top of the air handler.
Does it work??? Yes... and yes. Exterior sound is now like someone using a Hoover in a back room. Inside.... noise is reduced. Our RV was parked out in the sun a couple weeks ago for some maintenance and another 'mod.' At least 95F ambient in the direct sun. The Mach 8 'quietly' maintained a chilly 75F inside. Respectable performance.