Electric heating effects in the nematic liquid crystal change the liquid crystal physical properties and dynamics. We propose a model to quantitatively describe the heating effects caused by dielectric dispersion and ionic conductivity in the nematic liquid crystals upon the application of an ac electric field. The temperature increase of the liquid crystal cell is related to the properties of the liquid crystal such as the imaginary part of the dielectric permittivity, thermal properties of the bounding plates, and the surrounding medium as well as frequency and amplitude of the electric field. To study the temperature dynamics experimentally, we use a small thermocouple inserted directly into the nematic bulk; we assure that the thermocouple does not alter the thermal behavior of the system by comparing the results to those obtained by a noncontact birefringent probing technique recently proposed by Wen and Wu [Appl. Phys. Lett. 86, 231104 (2005)]. We determine how the temperature dynamics and the stationary value of the temperature increase depend on the parameters of the materials and the applied field. We used different surrounding media, from extremely good heat conductors such as aluminum cooling device to extremely poor conductor, Styrofoam; these two provide two limiting cases as compared to typical conditions of nematic cell exploitation in a laboratory or in commercial devices. The experiments confirm the theoretical predictions, namely, that the temperature rise is controlled not only by the heat transfer coefficient of the surrounding medium (as in the previous model) but also by the thickness and the thermal conductivity coefficient of the bounding plates enclosing the nematic layer. The temperature increase strongly depends on the director orientation and can change nonmonotonously with the frequency of the applied field.