Transparency, flexibility, and high thermal conductivity are trade-offs. Specifically, we have investigated a cross-linked acrylic liquid crystal elastomer (LCE) that exhibits both transparency and flexibility while maintaining a high level of thermal conductivity. The transparent monodomain LCE sheet was achieved through a process of stretching an initially opaque polydomain sheet to 80% elongation and subsequently subjecting it to photocuring. The thermal conductivity in the stretching direction (x) of the monodomain LCE sheet was found to be 1.8 times higher than that of the prestretched polydomain sheet, consistent with findings from previous studies. However, in the orthogonal direction (y) to the stretching (x) direction, the thermal conductivity exhibited an even higher value, being 1.7 times greater than in the x-direction, with a value of 3.0 W/(m·K). This unique observation prompted us to conduct further investigation through higher-order structural analysis of these LCE sheets using 2D wide-angle X-ray scattering (WAXS) analysis. In the transparent sheet, the LCE molecules were aligned in the sheet in the stretching x-direction (monodomain structure) for the out-of-plane direction. However, in the in-plane x-direction, the molecular plane spacing exhibited random orientation at a period of 0.45 nm. In contrast, within the y-direction of the inner layer, the molecular plane spacing exhibited a uniaxial horizontal orientation at the same period length as in the x-direction. The heat energy entering into the y-direction once spreads to the x-direction, but it was considered that the reason for the higher thermal conductivity to the y-direction would be forming covalent bonds that function as new heat transmission paths, in the direction intersecting to the x-direction during photocuring. Therefore, we concluded that the synergistic effect of the high level of the ordered inner structure and covalent bonding structure due to cross-linking in the y-direction contributes to its higher thermal conductivity compared to that in the x-direction, which exhibits a random in-plane structure. Additionally, we have fabricated an LCE composite sheet filled with 75 vol % of alumina particles using a polydomain-type LCE as the base material. The composite sheet exhibits remarkable thermal conductivity in the thickness direction, measuring at 9.8 W/(m·K), while maintaining a flexibility characterized by an elastic modulus of 70 MPa. This thermal conductivity surpasses that of a nonmesogenic acrylic composite sheet with identical alumina particle filling, which measured at 3.9 W/(m·K), more than twice as much. The presence of the mesogen skeleton has been demonstrated to enhance heat transfer, even within soft composites, by facilitating the formation of an ordered structure.