TEC 12706 not drawing more than 1.6A when powered by a 12V PC SMPS
Thermo-Electric Cooler efficiency "is a function of ambient temperature, hot and cold side heat exchanger (heat sink) performance, thermal load, Peltier module (thermopile) geometry, and Peltier electrical parameters." And "A single-stage TEC will typically produce a maximum temperature difference of 70°C between its hot and cold sides. The more heat moved using a TEC, the less efficient it becomes, because the TEC needs to dissipate both the heat being moved, as well as the heat it generates itself from its own power consumption."

So a heat sink on the "hot side" alone isn't enough. The cold side gets cold quickly, having little thermal mass, and efficiency falls to a very low value. Also as the hot side warms up, each junction's internal resistance increases, drawing less current. 

TECs are most efficient when both sides are the same temperature (and little heat is being moved.) The best overall working efficiency (in terms of pumping heat) may be up to about 13% of Imax. Beyond these currents, resistive heating losses increase greatly, and the device spends more power moving heat it generates itself.