The conductors are attempting to return to the electron equilibrium that existed before the current was applied by absorbing energy at one connector and releasing it at the other. The individual couples can be connected in series to enhance the effect. The direction of heat transfer is controlled by the polarity of the current, reversing the polarity will change the direction of transfer.
A Peltier cooler/heater or thermoelectric heat pump is a solid-state active heat pump which transfers heat from one side of the device to the other.
See also seebeck effect, the opposite effect - applying temperature gradient to generate current.
Peltier coolers are also called TECs (Thermo Electric Converter).