  We study heat conduction in a billiard channel formed by two sinusoidal walls
and the diffusion of particles in the corresponding channel of infinite length;
the latter system has an infinite horizon, i.e., a particle can travel an
arbitrary distance without colliding with the rippled walls. For small ripple
amplitudes, the dynamics of the heat carriers is regular and analytical results
for the temperature profile and heat flux are obtained using an effective
potential. The study also proposes a formula for the temperature profile that
is valid for any ripple amplitude. When the dynamics is regular, ballistic
conductance and ballistic diffusion are present. The Poincar\'e plots of the
associated dynamical system (the infinitely long channel) exhibit the generic
transition to chaos as ripple amplitude is increased.When no
Kolmogorov-Arnold-Moser (KAM) curves are present to forbid the connection of
all chaotic regions, the mean square displacement grows asymptotically with
time t as tln(t).
