Others have already stated that the tubing won't give off much heat. Sure it sees the same (roughly) fluid temperature as the radiator, but the fluid temperature is only part of the equation. Fluid to solid convection is many times more efficient that solid to air convection. This is why radiators have fins. The surface area of the fins will be many times that of the wetted solid to compensate for air's lower convection coefficient. This fact, combined with the relatively low conduction coefficient of tubing, means that the radiator really dominates the energy dissipation from our systems.
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