  New asymptotic models are formulated to capture the thermal transfer across
falling films. These models enable to simulate a wide range of Biot and Peclet
number values, without displaying nonphysical behaviors. The models correctly
capture the onset of the thermally developed regime at the inlet of the flow.
To evaluate the parameter space of acceptability, a comparison has been made
with the primitive equation solution for periodic boundary conditions, as well
as for an open flow with a periodic forcing at inlet. A good agreement is
obtained for moderate to high Peclet numbers.
