Blast, I are a thermoelectrics engineer. At least I was one at one point.

The challenge with thermoelectric power generation and cooling is that you need a material that has high electrical conductivity but low thermal conductivity. God saw fit to make most electrically conductive materials good heat conductors and most electrical insulators good heat insulators. Oh, by the way, the material needs to have a high Seebeck voltage as well.

[snip]

The real challenge in a consumer product is preventing overheating. Ferinstance, some "High Temp" modules start melting at only 200C.