In a piston aircraft engine, how much heat must be removed by the oil cooler? It is pretty straightforward to compute the heat and power generated by the combustion process, given the displacement, RPM and fuel mass flow rate. Similarly, the power exhausted can be computed with knowledge of EGT and conservation of mass.  The difference is dissipated as heat, from air cooling of cylinders and oil cooler.  I'm looking for a rough ratio between oil cooler and cylinder heat dissipation.
According to Fundamentals of Powerplants for Aircraft, quoted in Mike Busch on Engines (chapter 2), "Other thermal losses" account for 12.2% of fuel energy:


Conduction to air: 7.2%
Conduction to oil: 1.6%
Radiation and misc: 3.4%


The other two areas of loss are exhaust (51.6%) and mechanical (36.2%).

I don't know how "cylinder heat dissipation" would fit into this classification (some combination of air conduction and friction losses?), but looking only at conduction losses gives a ratio of air to oil of 4.5:1.