  In this paper, we study the nonlinear electrodynamics in the framework of
$f(T)$ gravity for FRW universe along with dust matter, magnetic and torsion
contributions. We evaluate the equation of state and deceleration parameters to
explore the accelerated expansion of the universe. The validity of generalized
second law of thermodynamics for Hubble and event horizons is also investigated
in this scenario. For this purpose, we assume pole-like and power-law forms of
scale factor and construct $f(T)$ models. The graphical behavior of the
cosmological parameters versus smaller values of redshift $z$ represent the
accelerated expansion of the universe. It turns out that the generalized second
law of thermodynamics holds for all values of $z$ with event horizon for
power-law scale factor whereas it holds in a specific range of $z$ with Hubble
horizon for power-law and both horizons in pole-like scale factors.
