I would be interested in where this came from as it does not sound logical to me .
Ash less oil is a EPA requirement for 2 stroke marine engines , particularly when used on inland waterways down here .
As ash is an oxide and as most oxides are refractory in nature I can not see how they would materially change the cooling of an engine.
I assume we have all sat around a campfire or two and noticed when the logs get a white ash layer on top of them the fire is noticeably cooler and needs a stir up or some more fuel .
Also in the morning the remaining charcoals are fairly cold but the ash is still quite hot and it retains this heat because it is refractory so it transfers heat into the air very very slowly the same as it adsorbs heat from the fire very very slowly .
On top of that, there is a very tiny amount of ash produced because there is a very tiny amount of ash creating compounds in 2 stroke oils
From memory ( so please correct me if this is wrong ) low ash generates 1% to 5% ash and no ash is less than 1% ( those definations were always being shifted back when I was involved in this stuff and way back then there was no legal defination , but that was quite a while ago ( I am 70 and last worked on oils better than 40 years ago ).
So in a big chainsaw with a 100cc engine with oil ratio of 50:1 running very rich ( for easy calculations ) on an air fuel ratio of 10:1 there would be 0.2ml of oil in each power cycle if we ignore what condenses in the crankcase and coats bearings to make things easier .
If we make it a high ash oil @ 10% ash ( for ease of mental maths ) then that 0.2ml of oil would produce 0.02ml of ash.
To visualise this the head of a plain drawing pin is around 0.1ml
Now while it is true that the burning of the compounds to create ash does take heat out of the burning charge, the actual amount of heat is miniscule compared to the heat passed through the piston rings into the bore which in itself is a small proportion of the heat that is passed out the exhaust.
The bulk of ash would have come from the Stoddard Solvent and calcium .
While we could go through the heat balance calculations , I have no idea what is in fuel now days so they would be meaningless.
But if you are relying on the ash to carry away heat to prevent it from overheating then you are running well over the design limits of that engine
