How can I check if cooling fan is working

Are you referring to the temperature sending unit? You need to check it for resistance.

1. Inspect cooling fan ECU.

A. Inspect the input voltage.

1. Disconnect the cooling fan ECU connector.

2. Turn the ignition switch to the "on" position. Check the voltage of the +B terminal of the disconnected wire harness side connector.
Standard voltage:
9 to 14 V

If the result is not as specified, inspect the power source system (fusible link, fuse, wire harness and relay).

B. Inspect the cooling fan motor (See On-vehicle inspection).

C. Measure the resistance between terminals RFC (ECM) and SI (cooling fan ECU) of the wire harness side connectors.

Hint:
If the fan does not operate, there may be a short circuit.
If the fan remains operating, there may be an open circuit.

D. Inspect the ECM power source circuit and ground circuit.