With the use of simple models, we investigated the optical conductivity of a nodal-line semimetal (NLSM) whose crossing of the conduction and valence bands near the origin ($O$ point) in the ($k_x,k_y$) plane of a small cubic region can be adjusted by a parameter $\alpha$. The Hamiltonian of the NLSM is based on the ${\bf k}\cdot {\bf p}$ model for the low-lying energy bands. When $\alpha=0$, these bands touch each other along a continuous closed loop but the opening of a band gap corresponding to finite values of $\alpha$ and the varying of the carrier concentration can be adjusted. This provides a tunable semiconductor gap, around the $O$ point and the valence and conduction bands can meet at a pair of points within the small cubic region in ${\bf k }$ space. The optical conductivity of such a NLSM is calculated using the Kubo formula with emphasis on the optical spectral weight redistribution, deduced from appropriate Green's functions, brought about by changes in gap and chemical potential due to modifying $\alpha$. We derived closed-form semi-analytic expressions for the longitudinal components of the optical conductivity for these model systems of NLSM and compare results for chosen $\alpha$ and chemical potential. We also present results for the heat capacity when the system is in thermal equilibrium for various chosen $\alpha$ and chemical potential.
