Currently, thermally excited magnons are being intensively investigated owing to their potential in computing devices and thermoelectric conversion technologies. We report the detection of thermal magnon current propagating in a magnetic insulator yttrium iron garnet under a temperature gradient using a quantum sensor: electron spins associated with nitrogen-vacancy (NV) centers in diamond. Thermal magnon current was observed as modified Rabi oscillation frequencies of NV spins hosted in a beam-shaped bulk diamond that resonantly coupled with coherent magnon propagating over a long distance. Additionally, using a nanodiamond, alteration in NV spin relaxation rates depending on the applied temperature gradient were observed under a non-resonant NV excitation condition. The demonstration of probing thermal magnon current mediated by coherent magnon via NV spin states serves as a basis for creating a new device platform hybridizing spin caloritronics and spin qubits.