Thermoelectric couple heating on both sides
In a sense it is working, by keeping one side cooler than the other. 

The problem is that you're not removing the heat from the hot side fast enough, so it's not getting colder than ambient on the cool side. If you allow it to get too hot you'll damage it. 

You need a BIG heatsink on the hot side for it to work. TECs are very inefficient, and you need to remove all the heat from the cool side, plus all the wasted heat you're pumping into it (which is much greater).