Yup. Oil coolers can get internally coated with a varnish over time. It doesn't wash out. I had a 172 consistently redlining the oil temp until I finally took the cooler off and replaced it with another one from another airplane in the fleet. Temps went to normal. Bought a new cooler.
If that oil temp system in the Aztec is electrical, be aware that oil temp indications can be hijacked by poor engine-to-airframe grounding. The electron flow for the gauge is from the engine case, through the thermistor, and through the wire to the gauge, then to the bus, through the battery to ground and back to the engine case. The alternator's charging flow is into the case, to airframe ground, though the battery to the bus and back through the cable to the alternator's positive terminal. Now, if the engine's grounding to the airframe is the least bit compromised, the electrons start looking for alternate paths to ground, and they find it in engine control cables and stuff like the gauge circuit. That boosts the gauge circuit current flow and makes the gauge read high.
Engine grounds are often compromised. They get dirty, loose, corroded, and sometime a mechanic doesn't even clean the paint off the engine case at the cable's grounding point. Sometimes the ground is only to the engine mount, which has problems of its own where it bolts to the firewall.
Cessna issued an SB on it years ago, and called for a small wire to run from the engine case close to the thermistor all the way to the gauge's case. This is to eliminate any electrical potential between the two. It's a patch, not a proper fix; the real fix is to clean up all the grounding. Eventually the ground could get bad enough that starter current begins to run through control cables and other stuff and fries them.
Bad ground points can be located by taking voltage drop measurements across the suspect areas while someone cranks the engine. The huge current flow across small resistances will cause significant voltage drops.
