This is a better idea than trying to equalize temperature through the shaft. Install a sight glass in the bearing housing. The oil level should be through the center of the bottom ball in the bearing when the pump shaft is not turning. Replace the bearing grease or lip seals that damage the shaft and allow moisture o penetrate into the bearing housing. Positive face seals should be your first choice, with an expansion chamber installed in the housing vent.
Labyrinth seals are an alternative, but they only work when the shaft is turning.
They are not very good on intermittent service pumps. Install a better thrust bearing retention method. It is possible to change the impeller to a different shape if you need to meet this number. Install an impeller inducer if you do not have enough NPSH available to prevent the pump from cavitating. Install a split mechanical seal to fix a leaking pump.