I thought mainly cars with turbos had oil coolers to cool oil that was heated up by the turbo.If it's cold out, thermostat operation will limit how much of the block coolant gets diverted to the rad, so rad bulk temps can be quite a bit different from engine bulk temps. So, if the oil is not on a thermostatically controlled circuit and getting cycled into the rad, if the rad is 15-20 degrees colder than the coolant in the block, that's going to reflect in oil temps.
On the other hand, applications with a block-mounted heat exchanger that uses block coolant as the heat transfer fluid, temps are going to be much closer coupled.
I would think you want to oil entering the block to be at engine operating temp to provide the best lubrication. You are not expecting the oil to provide any cooling. Maybe your oil cooler is cooling the oil too much.