if the C50 is similar to my friend's C90, the 'liquid' doing the cooling will be the oil itself thru a radiator-style oil cooler; my friend's C90 requires 4.7 quarts or liters of oil per change; he's settled on Suzuki's 10w-40 synthetic blend motorcycle oil made by SOPUS (Shell, Pennzoil, Quaker State) for the current and next oil changes; he tried Mobil 1 synthetic 20w-50 and didn't like the way it felt while shifting;
on the opposite end, my Honda Shadow 750 Aero is 'liquid' cooled with ethylene glycol based antifreeze/coolant and my oil sump requires 2.7 liters per change; I am using up a mixed stash of synthetic, synthetic blend, and conventional oils that have accumulated from the various motorcycles & scooters I have rotated thru over the past few years (Amsoil, Valvoline, Maxima, Shell Rotella T, etc in 10w-40 & 15w-40)