In the present work, the thermal conductivity and thermal expansion coefficients of a new morphology of Ni/graphene composites are studied by molecular dynamics. The matrix of the considered composite is crumpled graphene, which is composed of crumpled graphene flakes of 2–4 nm size connected by van der Waals force. Pores of the crumpled graphene matrix were filled with small Ni nanoparticles. Three composite structures with different sizes of Ni nanoparticles (or different Ni content—8, 16, and 24 at.% Ni) were considered. The thermal conductivity of Ni/graphene composite was associated with the formation of a crumpled graphene structure (with a high density of wrinkles) during the composite fabrication and with the formation of a contact boundary between the Ni and graphene network. It was found that, the greater the Ni content in the composite, the higher the thermal conductivity. For example, at 300 K, $\lambda$ = 40 W/(mK) for 8 at.% Ni, $\lambda$ = 50 W/(mK) for 16 at.% Ni, and $\lambda$ = 60 W/(mK) for 24 at.% Ni. However, it was shown that thermal conductivity slightly depends on the temperature in a range between 100 and 600 K. The increase in the thermal expansion coefficient from 5 × 10${}^{-6}$ K${}^{-1}$, with an increase in the Ni content, to 8 × 10${}^{-6}$ K${}^{-1}$ is explained by the fact that pure Ni has high thermal conductivity. The results obtained on thermal properties combined with the high mechanical properties of Ni/graphene composites allow us to predict its application for the fabrication of new flexible electronics, supercapacitors, and Li-ion batteries.