Here, in this work we establish the main cosmological parameters namely the deceleration parameter $q$, the equation of state parameter $w$ and the diagnostic omega $Om$ for $f(R)$ modified gravity using Sharma-Mitall Holographic Dark Energy model ($SMHDE$).Our model shows a type of stability of achieved by studying the behavior of the square speed of sound parameter which has a positive behavior over the given range . For the considered red shift $z$ range, we study the evolution of energy conditions for our model and the growth of dark energy the results fit the observations that the dark energy increase with time and the universe in an accelerated expansion epoch. Thermal analysis is considered through the quantum correction for power law and logarithmic entropy, consequently we study the validity of the generalized second law of thermodynamic the results show that the the generalized second law of thermodynamic holds using power law corrected scenario.