Thermoelectric cooler/generators can do two things.
1) Given a temperature differential (a hot thing and a cold thing), they can generate electricity from the natural flow of heat (that is, the natural flow of heat from the hot thing to the cold thing). They only work if there is a temperature difference, meaning that the hot side stays hot and the cold side stays cold, so you need a heat sink on the cold side, and a continuous supply of heat on the hot side. Because the thermoelectric junction is in the way of the heat flow, the hot side will always be hotter then if it were simply directly connected to the heat sink.
So if you have a Luxeon and a heat sink, putting the thermoelectric junction between them would make the Luxeon hotter, but would generate a bit of electricity.
The problem is that the efficiency of the thermoelectric junctions is quite low, and you might convert 5% of the wasted heat back into electric power. This recovered electricity would be balanced against the lower efficiency of the Luxeon because of the higher junction temperature.
2) Given an external supply of electric power, a thermoelectric junction can pump heat from one location to another, _against_ the natural flow of heat. This means that with an externally powered thermoelectric junction you could have heat flow from a cool region to a warmer region. For example, you could cool the Luxeon down to 0C in a 25C room.
You are consuming electrical power to move this heat around, but this would have to be balanced against the improved efficiency of the Luxeon because of lower operating temperature.
-Jon