This paper proposes a temporally-coordinated operation method for a multi-energy microgrid under diverse uncertainties from renewable energy sources, power loads and electricity transaction prices between the microgrid and the utility grid. The method aims to coordinate multiple energies in different timescales considering distinct properties of thermal and power energy: the combined cooling heat and power plants, power-to-thermal conversion units and thermal storage tanks are dispatched hourly in the day-ahead operation stage; in the intra-day online operation stage, the battery storage units are dispatched to supplement the day-ahead operation decisions every 5 min after the uncertainties are realized. Based on constraints linearization and uncertain scenario generation/reduction, the problem is converted to a deterministic two-stage mixed-integer linear programming equivalent model which can be solved efficiently. Finally, the proposed method is verified on an IEEE 33 bus distribution network based multi-energy microgrid. Compared with the existing methods, the simulation results indicate that the proposed method can better coordinate multiple energies with low operating cost and high robustness.