The current investigation employs Monte Carlo simulations to explore the magnetic features of a Fullerene-dimer-like nanostructure (C60)2 characterized by the spin σ-1. It explores how the coupling interaction Jσ, the biquadratic parameter K, the external magnetic H and the crystal D fields influence the thermal and magnetic features of the nanostructure, particularly the blocking temperature (TB). The results also highlight the dependence of hysteresis cycles and the coercive magnetic field Hc on the values of Jσ, K, and D, with significant variations at lower temperatures. The findings indicate the distinctive magnetic behavior of the Fullerene-dimer-like nanostructure (C60)2 potentially useful in various technological applications.