The first thing I would do is to isolate whether it is the brakes or the bearings that are causing the temperature differential. I would first use a digital infra-red thermometer (Radio-Shack, about $30) and establish an accurate temperature differential between the sides during normal use, taking into account the normal difference between the side in the sun and the side in the shade. Do a run travelling from east to west, and another from west to east. Then take the trailer out for another run when the wheels have cooled to ambient temperature. Go out at a quiet time on quiet roads, and try to avoid all use of the brakes. After ten minutes, drift to a halt without using the brakes, and measure the temperatures of the wheels. If there is still the same differential, you have a bearing problem (One adjusted tighter than the other, or one newer than the other). If no significant differential, you have a braking problem. (Incorrect parts fitted, or pull-off springs of differing strengths.) That's what I did in a similar situation, and it turned out to be incompatible parts in the brakes supplied by the Airstream dealer.
Nick Crowhurst, Excella 25 1988, Dodge Ram 2500 Cummins Diesel. England in summer, USA in winter.
"The price of freedom is eternal maintenance."