To reveal the dynamic characteristics of asphalt core embankment dams (ACEDs), we carried out a dynamic triaxial experiment on hydraulic asphalt concrete (HAC) under different temperatures (T = 4 °C, 10 °C, 16 °C, and 22 °C) and stress states (Kc = 1.0, 1.2, 1.4, and 1.6; σ3 = 0.5, 0.6, 0.7, and 0.8 MPa). The results indicate that HAC’s maximum dynamic elastic modulus increased with decreasing temperature, increasing principal stress ratio, and increasing confining pressure. However, the damping ratio showed the opposite trend. Moreover, in order to study the deformation capacity of HAC, 300 cyclic loads were applied to some specimens. At a temperature of 22 °C, the specimens had a tendency to deform axially, but not significantly. With a decrease in temperature, the axial deformation tendency of the specimen gradually weakened or even disappeared. However, a small number of cracks appeared in the aggregate and between the asphalt and the aggregate of the specimen. In order to quantify the dependence of dynamic parameters on temperature, the temperature influence factor of the maximum dynamic elastic modulus and the temperature sensing factor of the damping ratio were defined. The variation in the temperature influence factor of the maximum dynamic elastic modulus with temperature can be described by a logistic function. The temperature sensing factor of the damping ratio increased with an increasing principal stress ratio and peripheral pressure. Finally, maximum dynamic elastic modulus and damping ratio computational models for the interaction of temperatures and stress states were developed using the normalization method. Upon comparison, the dynamic parameters were observed to be very close to those listed in the literature, which verifies the applicability of the computational models of the maximum dynamic elastic modulus and damping ratio.