In a piston aircraft engine, how much heat must be removed by the oil cooler?
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.