Not saying there isn't a special washer, but the voltages generated will be cancelled out as long as both sides of the star washer are at the same temperature; which is pretty certain!
Additional thermocouple trivia/minutiae: Common misconception is that the thermocouple voltage is generated at the junction between the two different metals; that is NOT true. If you think about it, it can't be because you would have some, albeit small, voltage across close to zero ohms which would generate an enormous current!
The voltage is generated along the length of the two wires; since the wires are different metals, the voltages generated are slightly different. That difference is the thermocouple voltage. This is the reason for both aging and why there is 'thermocouple wire' and 'thermocouple extension wire' available. Thermocouple wire is highly purified and homogenous. Extension wire, not so much. The reason for aging is that the wire's remaining impurities migrate over time, in part due to the temperature difference along their length, and thus change the voltage generated. Thermocouple extension wire operates at a much lower temp (usually room temp) over its entire length.