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Temporal computing promises to mitigate the stringent area constraints and clock distribution overheads of traditional superconducting digital computing. To design a scalable, area- and power-efficient superconducting network on chip (NoC), we propose packet-switched superconducting temporal NoC (PaST-NoC). PaST-NoC operates its control path in the temporal domain using race logic (RL), combined with bufferless deflection flow control to minimize area. Packets encode their destination using RL and carry a collection of data pulses that the receiver can interpret as pulse trains, RL, serialized binary, or other formats. We demonstrate how to scale up PaST-NoC to arbitrary topologies based on 2x2 routers and 4x4 butterflies as building blocks. As we show, if data pulses are interpreted using RL, PaST-NoC outperforms state-of-the-art superconducting binary NoCs in throughput per area by as much as 5x for long packets.