If the oil temperatures goes up, either the cooling system isn't working properly or the the prop shaft is generating more heat.
So first check the cooling system, simple things first, are all the valves fully open, clean any filters, check the current drawn by the pump motor, it will INCREASE as the pump becomes worn and the water recirculates from the discharge side back to the suction side inside the pump, increasing the mass flow produced by the impeller even as the mass flow outside the pump falls, if you have no record of the motor current from before the problem started, you may have to open up the pump and check it.
Is there a thermostat? is that full open, bypassing the cooler or has the inside corroded away? ( I saw that on one ship where the crew had decided to dose the the Domestic Fresh Water with Swimming Pool Chlorine Tablets, the chlorine corroded away all the Brass thermostats in the Fresh Water Cooling systems and also the the Domestic Fresh Water pressure was maintained by pumping water continuously against a relief valve and the relief valve dissolved.
Have you logged readings of the oil and water temperatures before and after the cooler? Those might give a clue. Was the change in temperature sudden or gradual?
If the shaft is generating more heat, the friction has increased, so most likely either the bearings have failed or the shaft is bent, or the prop is out of balance, have you grounded or has the prop made contact with submerged debris or anything that might have caused prop damage?
Those are the things that I would be looking at.
It is always better to ask a stupid question than to do a stupid thing.