Low oil level only becomes a cooling issue when its seriously low. By then bearings are failing so its cooling ability is the least of your worries. Many cars have an oil to coolant heat exchanger so in the end its still down to the cooling system.
A pedantic clarification rather than trying to start an argument, but low oil will impact on coolant temps. This is not because of friction but because oil in the sump actually releases a lot of heat (try touching it after a run).
With insufficient oil, it is being recirculated through the engine more frequently (gaining more heat) and spending less time in the sump (releasing that heat). As a result, the engine runs hotter, and the coolant has to take up the strain. The effect can be about 5 degrees centigrade, depending on insatallation.
Under normal running, this just means the thermostat opens a bit more, and a barely distinguishable movement on the needle. But in one of the strees conditions when the thermostat is already open, the effect is more noticeable.
Manufacturers run a series of cooling tests for these stress conditions. these include:
- High speed
- Gentle climb at speed
- Steep climb
- Tickover (ie stationary in traffic)
- Heat sink (when you park up and switch it off - temps will rise before dropping)
All at max load capacity to stress the engine most. Effects vary depending on layout, and the effects can come from increased heat generation (engine working hard), airflow limited by road speed, and the water pump moving slowly due to the low engine speed. Every installation is different. Of course the biggest issue is air temp, and problems normally occur in summer heat. In the current cooler weather, you have a bigger problem and oil is just the icing on the cake.*
And of course you will have spotted the bigger issue. The already hot oil will provide less lubrication (and oil pressure will drop), and where it hits a hot spot in the engine it's more likely to break down and leave deposits. That's likely to make high coolant temps the least of your worries. So always make sure your oil is filled.
* My experience is from spending far too long analysing such tests for wolwide tests (and reading my O-level Geography text book to understand max temperatures in countries around the world)