The unique electrical and optical properties of liquid crystal (LC) dispersions with carbon nanotubes (CNTs) have gained interest because of the potential applications in industries like displays, sensors, and photonics. The main topic of this study is the investigation of carbon nanotube-smectic-A liquid crystal dispersion with a particular focus on the high resolution dielectric anisotropy of these materials. For carbon nanotube-smectic-A liquid crystal dispersion high resolution dielectric anisotropy has been measured and then, the temperature variation of the nematic order parameter has been produced in both nematic-isotropic (N-I) and nematic-smectic A (N-Sm A) phase transitions. Additionally, by using data from the dielectric anisotropy in the vicinity of nematic-smectic A transition, the upper limit for the latent heat  for all samples have been determined. In the literature, there are studies about the finding of the upper limit for the latent heat using different methods like a calorimetric method and the optical birefringence measurement. An opposed to calorimetric approaches, high resolution dielectric  data has been demonstrated in this work for the first time to be extremely adequate and provide a simple way to investigate the nematic-smectic A transition.