I would not recommend trying to reduce the thrust bearing temperature by changing the running position. Instead, I would try to understand why one out of three identical pumps would have a different thrust bearing temperature than the other two. A few possibilities occur to me.
First, I assume that the pump has a tilt pad thrust bearing with embedded temperature probes (RTD's or thermocouples). A subtle difference in how the probe is embedded can result in a substantial difference in the temperature reading. Specifically, if the probe is closer to the surface or if there is slight bulge in the surface babbet because of the way the machining was done you can see a higher temperature reading. It can also make a noticeable difference if the instrumented pad is in the upper half or lower half. If the bearing is not functioning correctly because of a hang-up of a leveling pad or uneven shimming of the bearing halves you could see a higher temperature reading. I recently found a thrust irregularity in a high pressure coker jet water pump (3600 psi) that was a result of a distorted cage assembly resulting in uneven pressure among the bearing pads.
Then I would consider any differences in the lube oil conditions to the three machines. If the flow of oil to this bearing housing is different than the others, it could account for the temperature difference. An incorrect orifice plate or a plugged passage within the housing could explain the difference. Many of these bearings use floating brass rings as oil retainers on each side of the thrust bearing assembly. If the rings in this pump are tighter than the other pumps, it could be passing less oil flow. These bearings often run flooded but not pressurized. Is there supposed to be an overflow port at the top of the housing to allow the excess oil to spill over to the radial bearing section of the housing?
I would be very concerned about the condition of the balance line and pressure reducing bushing. Based on your description, I assume you have opposed impellers with a balance line. If the pressure on the two seals is not close to the same, there could be a restriction in the balance line or an opened up pressure reducing bushing. If the pressure in the two seals differs much, this will translate into a thrust imbalance. For that matter, any bushing or wear rings problems could affect the relative thrust contribution of one or more stages. A check of the overall pump performance relative to the test curve could reveal a problem.
I keep coming back to my original point. I would first try to understand the difference before I would try to correct it with any change to the pump. And as Artisi noted already, unless the temperature difference is resulting in failures, it might not require any action. If you could give us more details about the pump such as model, history or service conditions, we might be able to provide more specific advice.
Johnny Pellin