The voltage is produced at the junction between the dissimilar metals,
not by their individual bulk. <clip>
Aack! The old thermocouple junction myth rears it's ugly head again!
You have this exactly backwards - thermocouple voltage is produced by
the temperature gradients in the bulk of the wires, not by the
junction. The junction merely provides an electrical connection which
allows the bulk gradients in between the measurement junction and
reference junction to be measured. In the above example with the
reference junction (the connection of the thermocouple wires to the
copper meter leads) at the same temperature as the measurement
junction (both in the ice bath), the net temperature gradient between
the junctions is zero degrees, regardless of any different
temperatures in the middle of any of the wires.
There is no known possible physical mechanism which can produce
thermocouple voltages at the junction. Voltage gradients and
temperature gradients are associated because the high thermal
conductivity of good electrical conductors is due to transport of high
energy electrons from the hotter side to the colder side, balanced by
lower energy electrons returning to hot side. Same current both
directions, but the hotter electrons "see" more resistance, hence
higher voltage drop in the hot to cold direction, amount differing
between metals but not direction. See also Wiedeman-Franz law.