You do not mention the profile of the vibration. For example if you are using a random on random profile, the peak G's can be 4 times the RMS value.
If you are just vibrating in an open loop mode, ie no control accelerometer, then I would look for a resonate condition. You can also examine...
I agree that the best place to measure the brg temp is on the raceway. Since you are finding different temperatures in the same design gearboxes, the loading must be different. How are the brgs mounted? Press fit?
I use Diester based greases in our gearboxs such as Aeroshell 12. It has a good temp range. The obvious question is, can you use an oil? This would give the best cooling for the gear teeth. If you can't seal the oil in, then a grease is required.
