You can check the temp switch with a multimeter. Connect the meter on each wire to the switch (after disconnecting them from anything else) and you should see the switch as open circuit until you heat it up (a heat gun should work), and then it should show closed circuit. I would check that before ordering a relay kit, as the temp switch is probably cheaper and if it's bad the relay still won't work. You can also check the relay by shorting the two wires connected to the temp switch, and the fan should run.
