  We investigate some cosmological features of the LCDM model in the framework
of the generalized teleparallel theory of gravity f(T) where T denotes the
torsion scalar. Its reconstruction is performed giving rise to an integration
constant Q and other input parameters according to which we point out more
analysis. Thereby, we show that for some values of this constant, the first and
second laws of thermodynamics can be realized in the equilibrium description,
for the universe with the temperature inside the horizon equal to that at the
apparent horizon. Moreover, still within these suitable values of the constant,
we show that the model may be stable using the de Sitter and Power-Law
cosmological solutions.
