i would suggest a google of Peltier efficiency before you go down that dead end path. you don't see Peltier's used to cool anything that is above ambient temp for good reasons.
you would need to apply 3w to a typical Peltier device to get 2w of cooling heat transfer that means you now have 5w of heat to dissipate.
The device you linked could never cope with the heat you need to dissipate either.