Low temperature differentials yield poor efficiency due to thermodynamics.
Theoretical max. Eff = 1 - Tc/Th
...where temps are in kelvin. What this translates to is that small, low temp differential power generation is usually not practical or cost effective. I'm coming up with about 5% theoretical efficiency between a 37C hand and a 20C room. And the reality is that the conversion efficiency using a peltier device will be substantially worse than that.
These are always fun projects to think about, but the reality of trying to generate the 5-10W to charge a phone or flashlight in a reasonable time usually renders them impractical.