This paper investigates the performance of a non-orthogonal multiple access (NOMA) enabled full-duplex (FD) device-to-device (D2D) communication network that is underlaid in the cellular uplink. The uplink cellular user is licensed to serve the BS. For improving spectrum utilization efficiency, it also concurrently relays D2D information in FD mode. The transmit powers of D2D nodes are chosen such that the cumulative interference at the BS is below the Interference Temperature Limit (ITL). Using the statistical channel knowledge and successive interference cancellation at the D2D nodes, an expression for the D2D throughput is derived in closed-form. Thereafter, using the approximate throughput expressions, a closed-form expression of ITL apportioning parameter is derived in closed form that maximizes the D2D throughput while ensuring desired quality of service at the BS. Computer simulations demonstrate accuracy of the derived expressions.