  This work is focused on the dissipative system describing the dynamics of an
extensible thermoelastic beam, where the dissipation is entirely contributed by
the second equation ruling the evolution of the temperature. Under natural
boundary conditions, we prove the existence of bounded absorbing sets. When
both the external body force and the heat source are time-independent, the
related semigroup of solutions is shown to possess the global attractor of
optimal regularity for all values of the external axial load. The same result
holds true when the rotational inertia is taken into consideration. In both
cases, the solutions on the attractor are strong solutions.
