lemme know if u don't understand. i tried to write in simple way.
When one end of the conductor is heated, free electrons gain KE and move towards the colder region
crating the different potential at two ends. At the junction of thermocouple different potential is
created due to the different electron density of the conductors.
If the junctions of a thermocouple are placed on different temperature then the electrons diffusion rate
is different and creates a different contact potential on the two junctions so the current flows through
the thermocouple. But, when the temperature of two junction is same then rate of diffusion is also
same hence no net current on the thermocouple.