Is it necessary to run a cooling hose from the baffling to the battery
and cool it?

The coolest air flow exiting the engine into the area behind and below the
engine is the flow from the oil cooler.  CHTs are 350-400F making hot air,
and oil temperatures are more like 150-200F with MUCH less heat being
dissipated.  I once calculated that the expected air temperature rise across
the oil cooler was less than 20F meaning the exhaust air is cool.  I know it
is inadequate for cabin heat.  So your location behind the oil cooler is
probably just fine.

However, heat kills batteries.  I put in twin Odyssey batteries.  Out here
in the wilds of Australia, these fellows are $300 each, so I ran a small
hose from the back top engine baffle into the battery box in the firewall
with the flow entering between the batteries hoping for a bit of life
extension.  How much I will gain is unknown, but it makes me feel good. Fred Moreno