Old fella, surely it depends on the total capacity of the oil system and efficiency of the cooler? The 2200 Jabiru engine set-up in my homebuilt aircraft certainly runs cooler on 2 litres than it does at the full 2.4, by a good 10 degrees. Therefore I run it at 2 litres in hot weather, a bit more in winter.
Some more advanced types - e.g. turboprops and jets - usually run the oil through a cooler that itself is cooled by fuel (it doubles to heat the fuel and prevent icing at high altitudes - very neat solution). In this setup, a drop in oil temperature will either precede or confirm a low quantity warning, often well before any pressure drop. I have personal experience of this on a Bae146 which happened to be the one in the fleet with no oil quantity gauges. Coming out of Port Hedland on a very hot evening, during the climb the oil temp started to steadily decrease. At the first flick of the associated pressure gauge, we pulled it back to idle, gave it a minute or two to stabilise and shut it down. There was some criticism from uneducated quarters in the Company at the time that this was an over-reaction because no limit had actually been reached, but they shut up soon enough. A bearing seal had let go and dumped most of the oil. Saved a huge repair bill, we did...