  In the frame work of Palatini approach to modified $f(R)$ theories of
gravity, we attempt to investigate the thermodynamic behavior of time-dependent
wormhole geometries. By considering an evolving wormhole spacetime, we find the
field equations in Palatini $f(R)$ gravity. The energy density and pressure are
redefined in order to satisfy the continuity equation. To discuss the
thermodynamic behavior, an expression for the variation of total entropy is
obtained. Then, we extend our discussions to apparent and event horizons of
evolving wormholes. We employ the radius of apparent and event horizons to
determine the validity of generalized second law (GSL) of thermodynamics which
states that the variation of total entropy is non-negative.
